lac 

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UC-NRLF 


OF  THE 
UNIVERSITY 

OF       f, 

CALIFOI 


PHYSICS 


CONDENSATION  OF  VAPOR  AS  INDUCED 
BY  NUCLEI  AND  IONS 


FOURTH  REPORT 


BY  CARL  BARUS 
Hazard  Professor  of  Physics,  Brown  University 


WASHINGTON,  D.  C.: 

Published  by  the  Carnegie  Institution  of  Washington 
2910 


CONDENSATION  OF  VAPOR  AS  INDUCED 
BY  NUCLEI  AND  IONS 


FOURTH  REPORT 


BY  CARL  BARUS 
Hazard  Professor  of  Physics,  Brown  University 


WASHINGTON,  D.  C.: 

Published  by  the  Carnegie  Institution  of  Washington 
1910 


CARNEGIE  INSTITUTION  OF  WASHINGTON 
PUBLICATION  No.  96  (PART  2) 


PHYSICS 
LIBRARY 


PREFACE. 


In  Chapter  I  of  the  present  publication  the  investigations  on  the 
residual  nuclei  of  pure  water  (compare  Carnegie  Institution  of  Washing- 
ton Publication  No.  96,  Chapter  V,  1908)  have  been  resumed  with  regard 
to  the  size  and  persistence  of  such  nuclei.  These  are  obtained  by  the 
precipitation  of  water  on  the  nuclei  of  pure  water  vapor,  in  a  dust-free 
fog  chamber,  by"  sudden  cooling.  The  fog  particles  so  produced  evaporate 
to  water  nuclei  on  compression,  the  number  of  the  latter  as  compared 
with  the  former  being  greater  as  the  evaporation  of  fog  particles  is  more 
rapid  and  as  their  size  is  larger.  In  the  extreme  case  nearly  50  per  cent 
of  the  fog  particles  were  represented  by  these  residual  water  nuclei.  It 
is  a  curious  observation  that  whereas  the  relatively  enormous  fog  particles 
of  pure  water  evaporate  at  once  beyond  the  range  of  visibility,  such 
evaporation  stops  in  cases  of  certain  of  the  invisible  water  particles  (0.5  to 
50  per  cent  of  the  total  number  of  fog  particles)  as  the  evaporation  is  more 
rapid  in  the  manner  specified.  The  remaining  fog  particles  evaporate 
completely.  It  was  impossible  to  detect  any  electrical  effect  due  to  rapid 
evaporation.  The  cause  of  these  phenomena  is  difficult  to  ascertain,  but 
it  may  be  suspected  that  it  is  associated  with  the  composite  nature  of  the 
molecule  of  liquid  water. 

The  first  part  of  Chapter  II  contains  further  studies  of  the  optics  of 
coronas.  It  was  shown  that  the  interference  phenomenon  superimposed 
upon  the  diffraction  phenomenon  in  the  case  of  coronas  may  be  treated  in 
a  way  similar  to  the  lamellar  grating,  consisting  of  a  uniform  succession  of 
alternate  strips  of  thin  and  thicker  transparent  glass.  Given  types  of 
coronas  are  reproduced  in  successively  increasing  size,  when  the  respective 
fog-particle  diameters  are  in  the  ratio  of  .  .  .  .  5,4,3,2,1,0.  The 
ratio  of  fog-particle  diameters  d  and  interference  plate  thickness  D  for  the 
same  color  minimum  in  the  interferences  and  a  film  of  water  is  d/D  =  n 
(n—i),  where  n  is  the  index  of  refraction  of  water.  The  experimental 
value  of  d/D  agrees  well  with  this.  It  must  therefore  be  possible  to  com- 
pute the  nucleation  corresponding  to  a  given  corona  purely  from  optical 
considerations  of  diffraction  and  interference,  as  indicated.  To  further 
verify  the  theory  suggested,  special  study  was  made  of  the  axial  or  inter- 
ference colors  of  coronas  by  the  aid  of  large  drum-shaped  chambers  2 
meters  long. 

The  coronas  obtained  with  electric  light  are  almost  too  complicated 
for  practice,  for  which  reason  a  part  of  the  mantle  of  a  Welsbach  burner 

in 


IV  PREFACE. 

has  usually  been  used  as  a  source  of  light.  Much  better  results  are 
obtained,  however,  by  the  use  of  the  virtually  monochromatic  mercury 
lamp  as  a  source.  This  is  sufficiently  intense  and  admits  a  more  definite 
optical  interpretation.  Experiments  are  therefore  given  in  the  second 
part  of  Chapter  II,  with  a  view  to  standardizing  these  simplified  coronas 
by  the  method  of  successive  exhaustions  and  phosphorus  nuclei. 

The  third  part  of  the  chapter  gives  an  account  of  further  progress  made 
in  increasing  the  efficiency  of  the  fog  chamber  by  reducing  its  size  com- 
patibly with  the  use  of  a  new  type  of  goniometer. 

In  an  endeavor  to  standardize  the  coronas  in  terms  of  the  nucleation 
involved,  by  the  aid  of  separate  small  sealed  aluminum  tubes  containing 
radium,  used  singly  or  in  groups,  very  little  progress  was  made,  because 
the  coronal  diameter  varies  as  the  sixth  root  of  the  intensity  of  ionization. 
The  experiments  of  Chapter  III,  however,  lead  to  certain  remarkable 
results  on  the  distribution  of  ionization  with  reference  to  the  position 
within  the  fog  chamber  of  the  sealed  aluminum  tubelets  (beta  and  gamma 
rays  being  in  question,  largely  the  latter). 

If  the  parts  of  the  fog  chamber  consist  of  different  materials  or  not, 
the  maximum  ionization  due  to  primary  and  secondary  radiation  rarely 
coincides  with  the  position  of  the  radium.  In  a  horizontal  cylindrical 
fog  chamber,  closed  at  one  end  and  open  for  exhaustion  at  the  other, 
the  maximum  ionization  is  found  to  move  from  the  closed  end  to  the 
exhaustion  end  as  the  radium  moves  from  the  closed  end  to  the  middle 
of  the  chamber.  As  the  radium  moves  further  the  maximum  remains 
near  the  exhaustion  end,  but  the  ionization  diminishes  in  marked  degree 
throughout  the  whole  chamber.  The  ratios  of  ionization  are  frequently 
greater  than  2  to  i.  To  obtain  maxima  of  ionization  near  the  middle 
of  the  chamber  the  sealed  radium  tube  must  be  near  the  closed  end. 
In  other  adjustments  even  minimum  ionization  was  produceable  in 
the  middle,  as  compared  with  the  ends.  It  appears  from  the  results  that 
it  is  possible  to  appreciably  displace  the  ions  during  the  period  of  ex- 
haustion, the  rate  of  reproduction  being  insufficiently  rapid  as  compared 
with  the  displacement. 

In  a  final  investigation,  Chapter  IV,  the  endeavor  is  made  to  stand- 
ardize the  coronas  in  relation  to  the  number  of  fog  particles  represented 
under  given  circumstances  of  exhaustion  by  aid  of  Thomson's  electron 
and  correlative  constants.  After  a  number  of  trials  the  first  successful 
method  consisted  in  making  a  closed  aluminum  tube,  containing  an  even 
distribution  of  radium,  the  core  of  a  cylindrical  condenser,  leaded  to  an 
inch  or  more  in  thickness  without.  This  core  was  suspended  axially  from 
fine  wire  leading  to  Dolezalek's  electrometer  for  the  measurement  of  the 
small  voltages  and  currents  involved.  The  core  in  question  was  then 
removed  from  the  electrical  condenser  and  put  into  the  axis  of  a  dust- 


PREFACE.  V 

free  fog  chamber,  where  the  nucleation  (ionization)  was  found  from  the 
constants  of  the  coronas  obtained  upon  exhaustion,  or  vice  versa. 

Using  the  method  which  depends  essentially  on  the  known  velocity  of 
the  ions  in  the  unit  electric  field  and  my  earlier  values  of  the  constants 
of  coronas,  a  few  rough  tests  of  the  charge  of  the  electron  gave  consistent 
values.  There  was,  however,  an  inherent  difficulty  of  great  importance, 
the  nature  of  which  has  already  been  referred  to — the  ionization  differs  in 
different  parts  of  the  fog  chamber  and  the  extreme  ratios  may  exceed  2 
to  i.  It  does  not  follow,  therefore,  that  the  mean  ionization  observed 
in  the  fog  chamber  is  the  same  as  that  obtaining  within  the  heavy  leaded 
electrical  condenser.  To  secure  this  identity  the  fog  chamber  itself  must 
be  the  condenser. 

The  method  was,  therefore,  varied  by  using  the  cylindrical  fog  chamber 
(glass  wet  within,  put  to  earth)  with  its  axial  core  of  charged  aluminum 
tube  both  as  an  electrical  condenser  for  the  measurement  of  current  and 
as  a  fog  chamber  for  the  measurement  of  ionization.  The  end  of  the 
aluminum  tube  within  the  fog  chamber  is  hermetically  sealed ;  the  other 
is  open  without  for  the  introduction  of  the  sealed  tubelets  containing 
radium.  By  properly  adjusting  these  along  the  axis  an  approximately 
uniform  ionization  within  the  fog  chamber  is  obtainable.  The  trials  made 
seemed  promising  enough  to  make  it  worth  while  to  repeat  the  determi- 
nation of  e  by  Thomson's  method,  using,  however,  the  mercury  lamp  as 
a  source  of  light  and  a  purely  optical  method  for  the  measurement  of  the 
nucleation  as  suggested  above.  Results  will  be  given  in  a  later  report. 

The  correlative  method  of  determining  e  in  terms  of  the  decay  con- 
stant of  the  ionization  has  also  been  tried.  If  N  be  the  number  of  ions 
in  the  fog  chamber  due  to  the  radium  in  the  aluminum  tube  when  the 
latter  is  not  charged  and  n  the  number  when  it  is  charged  the  constant  e 
may  be  written 

e  =  CV/(b(N2-n*)v) 

where  C  is  the  capacity  and  v  the  volume  of  the  cylindrical  condenser 
fog  chamber  and  V  the  (constant)  fall  of  potential  of  the  core  per  second, 
due  to  the  current  passing  through  the  ionized  air  within  the  chamber. 
In  this  case  very  large  potentials  (250  volts)  may  be  used,  and  a  graduated 
Exner  electroscope  suffices  for  the  measurement  of  V. 

The  experiments  by  the  decay  method  in  the  second  part  of  Chapter 
IV,  made  for  the  present  merely  to  test  the  standardization  of  the  fog 
chamber,  as  detailed  in  the  earlier  publications  of  the  Carnegie  Insti- 
tution of  Washington,  nevertheless  lead  to  very  acceptable  values  of 
e,  even  at  the  enormous  ionizations  (exceeding  500,000  nuclei  per 
cubic  centimeter)  employed. 

The  values  for  e  in  Chapter  IV  were  too  high,  even  with  the  admission 
that  negative  ions  only  are  caught  in  the  fog  chamber  employed.  The 


VI  PREFACE. 

method  is,  therefore,  repeated  in  Chapter  V  with  greater  detail.  Con- 
denser and  fog  chamber  are  now  identical,  and  the  data  obtained  are  of 
reasonable  value. 

In  Chapter  VI,  finally,  the  effect  of  incidental  voltaic  contacts  occur- 
ring in  Chapter  V  is  critically  studied,  with  a  view  to  using  a  condenser 
whose  parts  are  of  different  metals  separated  by  an  ionized  medium  for 
the  measurement  of  voltaic  potentials. 

My  thanks  are  due  to  Miss  Laura  C.  Brant  for  efficient  assistance 
throughout  the  course  of  this  work. 

CARL  BARUS. 
BROWN  UNIVERSITY, 

Providence,  R.  /.,  August  i,  1909. 


CONTENTS. 


CHAPTER  I. — Nuclei  of  Pure  Water. 

Page. 

1.  Introductory i 

2.  Rapid  evaporation  of  fog  particles.    Phosphorus  nuclei.    Table  i ;  fig.  i i 

3.  Spontaneous  evaporation  of  fog  particles.    Phosphorus  nuclei.    Table  2 3 

4.  Slow  spontaneous  evaporation  of  fog  particles,    yapor  nuclei.    Table  3 4 

5.  Rapid  evaporation  of  fog  particles.    Vapor  nuclei.    Table  4 7 

6.  Evaporation  retarded  as  the  diameter  of  fog  particles  decreases 8 

7.  Time  losses.    Table  5 8 

8.  Effect  of  changes  of  the  drop  of  pressure 10 

9.  Exceptionally  rapid  evaporation 1 1 

10.  Conclusion 1 1 

1 1 .  The  same,  continued 12 

1 2.  The  same,  continued , 13 

13.  The  same,  continued 13 

14.  Statistical  hypothesis 14 

CHAPTER  II. — Standardization  and  Efficiency  of  the  Fog  Chamber. 

AXIAL,  COLORS   AND   INTERFERENCES. 

15.  Introductory 15 

16.  Causes  of  axial  colors.    Table  6 15 

17.  The  lamellar  grating 16 

18.  Disk  colors  of  coronas 16 

19.  Experiments  with  long  tubes.    Table  7 ;  fig.  2 17 

20.  Short  tubes.    Table  8 19 

CORONAS  WITH   MERCURY   LIGHT. 

21.  Preliminary  survey 20 

22.  Apparatus 21 

23.  Equations 21 

24.  Data  with  white  light.    Table  9 ;  fig.  3 22 

25.  Data  with  green  mercury  light.    Tables  10  and  1 1 ;  figs.  4  to  9 24 

26.  Inferences.    Interference  and  diffraction.    Table  12 31 

EFFICIENCY    OF    LARGE    AND    SMALL    FOG    CHAMBERS    ATTACHED    TO    THE 
SAME   VACUUM   CHAMBER. 

27.  Fog  chambers 33 

28.  Data.    Table  13;  fig.  10 34 

29.  Data  for  apertures.    Table  14;  fig.  1 1 37 

30.  Results 39 

31.  Conclusion 39 

CHAPTER  III. — Regions  of  Maximum  lonization  and  Miscellaneous 
Experiments. 

REGIONS   OF   MAXIMUM   IONIZATION   DUE   TO   GAMMA   RADIATION. 

32.  Introductory 41 

33.  Short  fog  chamber 41 

34.  Behavior  after  removal  of  radium 42 

35.  Long  fog  chamber 43 

36.  Data.    Table  15;  figs.  12  to  15 43 

37.  Inferences » 47 

VII 


Yin  CONTENTS. 

MISCELLANEOUS   EXPERIMENTS.  Page. 

38.  Experiments  to  detect  the  region  of  positive  ions.    Table  16;  fig.  16 48 

39.  Radium  within  the  fog  chamber.    Sealed  tubes.    Table  17 50 

40!  Distance  effect.    Table    18 51 

41.  Attempt  to  calibrate  the  fog  chamber  with  five  separate  sealed  tubelets  of 

radium.    Tables  18  and  19 ,  51 

CHAPTER  IV. — The  Standardization  of  the  Fog  Chamber  by  Aid  of  Thomson's 

Electron. 

THE   CONSTANT   6,    EXPRESSED   IN   TERMS   OF   VELOCITIES   OF  THE    IONS. 

42.  Advantages 54 

43.  Plate.    Fig.  17 54 

44.  Cylinder.    Fig.  18 55 

45.  The  same.    Preliminary  data.    Table  20 56 

46.  The  same.    Wires  surrounded  by  earthed  pipes 57 

47.  Conclusion 58 

THOMSON'S  CONSTANT  e,  EXPRESSED  IN  TERMS  OF  THE  DECAY  CONSTANT 

OF    IONS    WITHIN    THE    FOG    CHAMBER. 

48.  Introductory 59 

49.  Electrical  condenser  fog  chamber 59 

50.  Auxiliary  condenser 60 

5 1 .  Methods 6 1 

52.  Data  disregarding  external  gamma  rays.    Table  21 61 

53.  Further  data.    Table  22 63 

CHAPTER  V. — The  Electron  Method  of  Standardizing  the  Coronas  of  Cloudy 
Condensation  in  Terms  of  the  Velocities  of  the  Ions. 

54.  Introductory 65 

55.  Apparatus.    Fig.  19 65 

56.  Auxiliary  electrical  condensers 66 

57.  Methods  pursued 67 

58.  Data.    High  ioriization  currents.    Table  23 , 69 

59.  The  same.    Coronas 70 

60.  The  same.     Summary.    Figs.  20  and  21 71 

61.  Data.    Moderate  ionization.    Electrical  currents 72 

62.  The  same.    Coronas 72 

63.  The  same.    Summary.    Figs.  22  and  23 72 

64.  Data.    Small  ionizations.    Electric  currents 74 

65.  The  same.    Coronas 74 

66.  The  same.    Summary.    Figs.  24  and  25 74 

67.  Conclusion 75 

CHAPTER  VI. — Electro  metric  Measurement  of  Voltaic  Potential  Difference 
between  the  Conductors  of  the  Condenser  Separated  by  an  Ionized 
Medium. 

68.  Introductory.    Fig.  26 76 

69.  Theory 78 

70.  Data.    Origin  of  the  electrometer  current.    Fig.  27 80 

71.  Aluminum  core  charged  with  radium  tubelets.    Table  24;   fig.    28 82 

72.  Results.    Ionization  and  voltaic  contact  potential  difference 82 

73.  Voltaic    contacts:    aluminum-zinc,    aluminum-copper,    aluminum-aluminum. 

Table  25 ;  fig.  29 82 

74.  Further  experiments  and  conclusion 83 


CHAPTER  I. 
NUCLEI  OF  PURE  WATER. 

1.  Introductory. — In   case   of  a   fog   chamber  but   4   cm.   high   and 
broad  and  lined  with  wet  cloth,  I  was  surprised  to  find  that  if  each  of  a 
succession  of  fogs  precipitated  on  phosphorus  nuclei  is  allowed  to  (appar- 
ently) subside,  i.  e.,  to  be  completely  dissipated  without  influx  of  air 
before  the  next  exhaustion  is  made,  it  nevertheless  takes  about  10  or  12 
exhaustions  before  all  the  nuclei  are  precipitated.     It  follows,  therefore, 
that  for  very  small  fog  particles  the  dissipation  by  evaporation  in  origin- 
ally* saturated  air  is  enormously  more  important  than  the  dissipation 
by  subsidence.     The  fog  particles  do  not,  however,  vanish  completely, 
but  the  evaporation  terminates  in  persistent  solutional  water  nuclei, 
large  enough  to  keep  the  air  bluish  or  hazy. 

If  the  same  experiment  is  made  with  rigorously  dust-free  air  and  vapor 
nuclei,  the  fog  particles  vanish  almost  completely  in  a  single  slow  evapor- 
ation, so  that  but  one  additional  exhaustion  is  needed  to  quite  clear  the 
fog  chamber.  Very  few  water  nuclei  (several  per  cent)  are  left  behind  in 
this  case.  The  number  increases  when  the  evaporation  is  more  and  more 
accelerated  by  the  rapid  influx  of  dust-free  air. 

It  is  this  feature  of  the  experiment,  the  tendency  of  the  water  nuclei  left 
after  precipitation  of  dust-free  wet  air  on  the  vapor  nuclei  of  its  own 
medium  to  persist  in  proportion  as  the  evaporation  is  faster  (more  or  less 
compression  or  rise  of  temperature) ,  that  is  the  chief  burden  of  the  present 
paper.  The  fact  that  water  nuclei  may  persist,  while  the  enormously 
larger  fog  particles  from  which  they  have  been  obtained  all  but  evaporate, 
is  the  interesting  part  of  this  result.  Some  restraining  tendency!  must 
therefore  be  evoked  by  which  the  accelerating  effect  of  convexity  is  much 
more  than  canceled,  for  the  nuclei  here  in  question  are  produced  in 
rigorously  dust-free  air  by  the  precipitation  of  water  vapor  on  water 
vapor.  A  solutional  effect  is  therefore  absent. 

To  investigate  the  question  it  is  expedient  to  begin  with  a  medium  of 
phosphorus  or  solutional  nuclei,  to  subject  the  fogs  thereupon  to  more  or 
less  rapid  evaporation,  and  thereafter  to  compare  these  results  with  the 
corresponding  case  for  vapor  nuclei. 

2.  Rapid  evaporation   of   fog   particles.     Phosphorus   nuclei. — In  the 

following  experiments  I  have  endeavored  to  trace  these  results  quantita- 

*Probably  the  rise  of  temperature  is  sufficiently  rapid  to  render  saturated  air  from 
which  a  fog  has  been  precipitated  temporarily  unsaturated. 

fThe  earlier  work  has  been  quoted  in  Part  I  of  Publication  No.  96,  Carnegie  Institution 
of  Washington. 


2    CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 

lively.  For  this  purpose  fog  particles  precipitated  on  phosphorus  nuclei 
were  successively  evaporated  as  rapidly  as  possible  by  compression 
(influx  of  air),  so  as  to  make  the  loss  by  subsidence  negligible  except  at 
the  end  of  the  series,  when  so  few  nuclei  are  present  that  the  precipitate 
is  rain-like.  In  such  a  case  the  only  loss  of  nuclei  is  due  to  the  exhaustion, 
as  the  normal  time  loss*  is  relatively  small.  In  table  i,  taken  from  an 
earlier  report,!  I  have  given  a  typical  case,  the  exhaustion  ratio  being 
^  =  0.78,  nearly.  As  dust-free  air  is  introduced  after  each  exhaustion  the 
successive  nucleations  are  clearly  in  geometric  progression.  As  long  as 
the  nucleation  is  less  than  100,000,  subsidence  may  be  disregarded,  as  the 


0&4.68J0 

FIG.  i. — Chart  showing  the  survival  ratio,  n'/n,  in  successive  exhaustions,  for 
phosphorus  nuclei  (.4,  2,  3,)  and  water  nuclei  (4,  5,  6,  7).  Scale  of  latter  magni- 
fied ten  times. 

curves  A  in  fig.  i  show.  The  table  also  contains  the  angular  diameters 
(£=5/30  of  the  coronas  and  the  nucleations  n  computed  therefrom.  Finally 
the  ratios  nf  /n  of  the  successive  nucleations  n  and  n'  are  given  in  each 
case.  These  should  be  equal  to  the  exhaustion  ratio  if  no  other  loss  of 
nuclei  occurs.  In  fact,  if  we  take  the  data  above  n=  100,000  the  mean 
ratio  of  the  ten  cases  is  n'/n  =  o.'j6,  agreeing  practically  with  ^  =  0.78. 

If  we  plot  the  successive  ratios  n' In  in  terms  of  n,  the  results  show  a 
jagged  curve  oscillating  about  n'/n  =  o.'jS,  but  descending  rapidly  below 
n  =  i o5  as  the  result  of  subsidence.  (Compare  curve  A ,  fig.  i .)  The  irreg- 
ularity of  the  curve  is  inevitable,  as  it  corresponds  to  a  ratio  between  two 
large  coronas  whose  outlines  are  no  longer  sharp ;  but  there  is  compen- 
sation in  the  successive  values,  as  the  curve,  taken  as  a  whole,  indicates. 

*Compare  chapter  n. 

tCarnegie  Institution  of  Washington  Publication  No.  96,  chap,  in,  table  17,  1908. 


NUCLEI    OF    PURE    WATER. 


i. — Quick  evaporation.    (Reproduced  from  Carnegie  Institution  of  Washington 
Publication  No.  92,  chap,  in,  table  17,  1908.)     y  —  o-779- 

SERIES  A. 


Corona. 

s. 

wXio-3. 

Ratio  n'/n. 

Corona. 

s. 

wXio-3. 

Ratio  n'/n. 

w  r 

1500 

0.67 

g 

7.8 

100 

0.69 

w  v 

.  . 

IOOO 

•7i 

o 

7-5 

89 

•74 

sb 

.    .  . 

7i5 

•91 

6.8 

66.5 

.65 

bp 

.    .  . 

650 

.89 

5-9 

63.0 

•57 

g 

580 

•79 

4-9 

24.6 

.66 

gy 

13 

460 

.70 

4.2 

16.3 

•53 

w  o 

«.  7 

320 

.78 

3-4 

8.7 

•35 

w  r 

10.5 

250 

.60 

2.4 

3-0 

.40 

w  p 

9-o 

152 

.67 

1.8 

1.2 

3.  Spontaneous  evaporation  of  fog  particles.  Phosphorus  nuclei. — With 
the  above  data  one  may  now  compare  the  corresponding  cases  for  very 
slow  evaporation,  in  which  the  fog  has  disappeared  spontaneously  in  the 
lapse  of  time,  apparently  by  subsidence,  but  in  greater  measure  by 
evaporation.  Part  i  of  table  2  shows  the  results  obtained  in  a  very  long 
(2  meters)  brass  tube,  lined  with  wet  cloth  but  4  cm.  high  and  broad. 
Twelve  exhaustions  are  needed  for  removing  the  nucleation,  in  spite  of 
the  spontaneous  disappearance  of  each  individual  fog.  The  disappointing 
feature  about  these  experiments  with  2 -inch  tubes  is  the  total  absence  of 
disk  or  axial  color  throughout.  They  were  made  in  the  hope  that  such 
colors  would  appear. 

In  parts  2  and  3  of  the  table  these  observations  are  continued,  but  now, 
with  a  glass  fog  chamber,  where  the  line  of  vision  passes  through  but  8  cm. 
of  fog  as  compared  with  200  cm.  above.  The  exhaustion  ratio  is  y  =  0.78, 
as  in  table  i .  Besides  the  disk  color  of  coronas,  the  successive  nucleations 
n  and  the  nucleation  ratios  nf /n  are  given.  These  ratios  are  also  con- 
structed in  fig.  i  in  terms  of.  n,  in  the  curves  2  and  3  of  the  chart.  Not- 
withstanding the  complete  apparent  subsidence,  nine  exhaustions  are 
needed  to  clean  the  fog  chamber  of  these  solutional  nuclei ;  but  the  effect 
of  subsidence  is  here  unmistakable  at  least  below  n=  io6  nuclei  per  cubic 
centimeter.  From  a  smooth  curve,  embodying  series  2  and  3,  the  sub- 
sidence effect,  together  with  other  permanent  loss,  may  be  stated  as 
follows  (3^  =  0.78).  The  approximate  diameter  is  d. 


Evapora- 

io6d 

io~3n 

Exhaustion 
loss. 

n'/n. 

Subsidence 
loss. 

tion  to 
water 

nuclei. 

cm. 

164 

1500 

0    22 

0.76 

O.O2 

0.98 

189 

IOOO 

22 

.68 

.10 

.90 

203 

800 

22 

•63 

•15 

.85- 

225 

600 

22 

•56 

.  22 

.78 

255 

400 

22 

.48 

•30 

.70 

320 

200 

22 

•30 

.48 

.52 

CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


From  these  data  it  appears  that  above  n=  200,000  nuclei  dissipation 
is  due  more  and  more  largely  to  evaporation;  below  n  =  2  X  io5  more  and 
more  largely  to  subsidence.  Above  w=io5  or  ^  =  0.003  cm.,  moreover, 
the  tube  in  part  i  remains  permanently  hazy  and  the  fogs  (if  seen  through 
some  thickness)  quite  black. 

TABLE  2. — Persistence  of  solutional  water  nuclei.     Shows  number  of  exhaustions  to 
clean  with  complete  (apparent)  subsidence. 


Exhaus- 
tion No. 

Corona. 

wXio~3 

-D   ,  .       1  Exhaus- 
Rat10'      tionNo. 

Corona. 

wXio-3 

Ratio. 

Part  i.  —  Phosphorus  emanation.     Long  brass  tube;    length  200  cm.;    diameter  5 
cm.;  cloth  lined.    Barometer  77.15  at  20°.    d/>3=  17  cm.,  about.    Each  fog  appar- 
ently falls  out.    Time  consumed,  about  30  minutes. 

2 

3 
4 

6 

black 
black 
black 
translucent 
fawn 
fog 



7 
8 

9 

10 

ii 

12 

corona 
corona 
corona 
faint  cor. 
very  faint 
very  faint 



Part  2,  series  2.  —  Glass   fog  chamber    (observations   transverse);    length   45   cm.; 
diameter  1  2  cm.  ;   height  of  cloth  8  cm.    Each  fog  allowed  to  fall  out  or  dissipate. 
Two  sources.    Barometer  77.75  at  20°.     £/>3=i7;   dp3/p  =  o.2os.    Time  consumed, 
27  minutes.    Fogs  dissipate  into  blue  haze. 

i 

2 

3 
4 

6 

Fogr' 
Fogr' 
Fog  c' 
Fog  v 

g 
s=  12;   o 

1700 
1400 

IOOO 

600 
400 

0.82 
.72 
.60 
.67 

•37 

7 
8 

9 

10 

ii 

12 

J  =  9I   g 
s  =  s;  cor. 
,$•=15;   cor. 

150 
46 

2 

0.31 
.04 

Part  3,  series  3.  —  Repeated.     Same  glass  fog  chamber.     Same  time,  about.    No.  4 
still  evaporates  to  blue  haze. 

i 

2 

3 
4 

5 

Fog 
.9=163;  r 
.r=i47;  c 
^=143;   gb 

^=130;  gy 

1700 
1400 

800 
500 

0.83 
•57 
•63 
•50 

6 

8 
9 

s=io5;  c 
^=70;   cor. 
.$•=27;  cor. 
s=io;  cor. 

250 
125 

7 

2 

0.50 
.06 
•03 

4.  Slow  spontaneous  evaporation  of  fog  particles.    Vapor  nuclei. — We 

may  now  contrast  with  the  preceding  the  evaporation  of  fog  particles 
precipitated  on  the  vapor  nuclei  of  dust-free  air.  Table  3  contains  the 
results  arranged  on  a  plan  similar  to  the  above.  A  slight  difference  of  pro- 
cedure is  necessary,  because  the  vapor  nuclei  are  not  caught  in  sufficient 
quantity  except  at  very  high  exhaustion.  Moreover,  these  exhaustions 
have  no  effect  in  removing  vapor  nuclei,  as  these  are  instantly  reproduced 
by  the  kinetic  mechanism.  The  water  nuclei,  however,  should  be  pre- 
cipitated at  an  exhaustion  less  than  the  fog  limit  of  dust-free  air.  Beyond 
this  the  exact  value  of  the  exhaustion  ratio  ^  =  0.71  to  o.  7  7  is  of  no  import- 
ance, because  the  ratio  of  successive  nucleations,  n'/n  is  usually  less  than 


NUCLEI    OF    PURE    WATER. 


i  per  cent,  showing  that  almost  all  nuclei  have  vanished  in  the  first 
evaporation  of  the  corresponding  fog  particles.  The  curves  Nos.  4  and  5  , 
fig.  i  ,  give  these  results  on  a  scale  ten  times  larger  than  the  preceding,  to 
bring  out  the  small  values  n'  /n,  which  would  vanish  on  the  scale  adopted 
for  the  solutional  nuclei.  For  reasons  which  do  not  clearly  appear,  the 
data  in  series  4  are  larger  than  corresponding  results  in  series  5  ,  possibly 


3.  —  Persistence  of  water  nuclei  when  fogs  are  precipitated  on  vapor  nuclei. 
Glass  fog  chamber.  d/>3=32  for  vapor  nuclei;  dp*=  22  or  23  for  water  nuclei.  Lower 
dp  =  22  or  23  is  above  fog  limit,  but  vapor  nuclei  are  inactive. 


to 

Corona. 

wXio-3 

Ratio. 

#i 

Corona. 

wXio-3 

Ratio. 

Part  i,  series  4.  —  Barometer  77.75  at  20°. 

32 

22 

^=108;   o 
^2  =  3o 

720 
12.4 

0.017 

42 
23 

^1=150;  g 
Ja  =  25 

2170 

6.9 

0.003 

36 

^=120;  y 
*«-3« 

1080 
13-3 

0,012 

Part  2,  series  5.  —  Repeated  in  glass  fog  chamber.     Barometer  75.77  at  22°. 

39 
17 

^1=130;  g 
^2=20 

1370 
3-0 

O.OO2 

27 
17 

*i  =  45 

S2=I2 

47 
•5 

O.OOI 

36 
17 

*i=i2o;   g 
*2=24 

*iO9O 
5-i 

.005 

28 
17 

^  =  84;   p 

S2=I2 

320 

•  5 

.002 

32 
17 

^1=122;   g 

*2=I9 

ti030 

2.6 

.002 

28 
17 

^1=85;  p 
*2=25 

326 

5-5 

.007 

29 
17 

sl  =  1  1  1  ;  r  o 

-5>2=25 

780 

5-5 

.007 

*Long  waiting  (3om)  for  s2.         fNo  waiting  ( im)  for  *2- 

because  the  exhaustion  in  the  former  case  was  above  the  fog  limit  of  dust- 
free  air  and  would  therefore  catch  the  smaller  order  of  water  nuclei  than 
occur  in  series  5.  These  water  nuclei,  in  fact,  are  reduced  appreciably  in 
number  in  the  lapse  of  time,  as  will  be  seen  by  comparing  the  two  experi- 
ments for  n  =  320, ooo  nuclei  in  series  5.  The  following  exhibit  may  be 
regarded  as  a  smoothed  curve  for  about  the  same  period  of  dissipation. 
The  curves  rise  for  smaller  nucleation;  the  exhaustion  loss  is  0.23. 


Number 

I0«d 

io~3n 

n'  /n 

Complete 
evaporation. 

completely 
evaporating 

Subsidence 
loss  above. 

per  cm3. 

cm. 

1  60 

1500 

0.003 

0-75 

1050 

0.02 

190 

IOOO 

.006 

.66 

660 

.  IO 

200 

800 

.007 

.61 

490 

.15 

220 

600 

.008 

•54 

320 

.22 

250 

400 

.009 

.46 

185 

•30 

320 

200 

.010 

.28 

56 

.48 

CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


This  accentuates  the  effect  of  subsidence,  which  with  the  exhaustion 
evaporation  must  account  for  the  total  number  of  nuclei  removed.  At 
first  sight  it  would  appear  that  the  number  of  residual  nuclei  is  inde- 
pendent of  the  number  of  vapor  nuclei  present,  as  if  some  other  nuclei 
which  may  accompany  the  vapor  nuclei  were  responsible  for  residual 
water  nuclei. 

4. — Case  of  rapid  evaporation  by  compression  (influx  of  dust-free  air). 


dp 

Corona. 

s 

Corona 
dissipated  by  — 

dp/p 

wXio-3 

Ratio. 

Part  i,  series  6.  —  Barometer  76.86  at  23.5°.    Time  between  exhaustions,  5  min- 
utes, usually.     Curve  No.  6,  fig.  i. 

35-7 
18.5 

28.7 
18.5 

28.7 
18.5 

28.7 
18.5 

30-5 
18.5 

30.5 
18.5 

32.2 
18.5 
32.2 
18.5 

*Time 

r  o 
corona 

w  b  p 
corona 

wb  p 
corona 

y 

corona 

P 
corona 

P 
corona 

r 
corona 

r 
corona 

interval  b 

u.  8 
6.0 

9.0 

2.8 

8.5 
5-3 

8.0 
4-5 
ii  .0 
5-6 

IO.O 

3-5 
10.5 
5-5 
10.7 

5-2 

etween  ot 

\  Compression  .  . 

r    0.465 
\      .240 

(         -373 
\          .240 

['        -373 
I          -240 

/          -373 
\          .240 

/          -397 
\          .240 

/          -397 
\          .240 

r      .420 
\      .240 

.420 
.240 

;.     y=o.75 

600 

49 

220 

5 

190 

33 
1  60 

21 

355 
39 

*27O 
*IO 

*320 

*37 
340 
3i 

|      0.082 
1         .023 

}     .,„ 

}         -130 

>             .110 

}         -037 

}     .«, 

}         -091 

>  Slow  evaporation. 
>  Compression  

)  ....Do... 

I 
\        Do 

r 

\  Evaporation*  
>  Compression* 

•servations  3  minutes 

Part  2,  series  7.  —  Green  coronas.    No  subsidence.    Barometer  76.70  at  22°.    Time 
between  exhaustions,  3  to  5  minutes.     Temperature  25°.     Curve  No.  7,  fig.  i. 

dp 

Corona. 

j 

Fog 
dissipated  by 

dp/p 

nX  io-3 

Ratio. 

36 

18 

36 
18 

36 
18 

36 

18 

36 
18 

g 
br  b  p 

gbp 

gbp 

g 
corona 

g 
corona 

16.0 
5-6 

16.0 
5-6 

16.0 
5-6 

16.5 
1.8 

16.0 

4-5 

1  Compression  or 
/  influx 

I       0.470 
\         .240 

r      .470 
\      .240 

r      .470 
\      .240 

r     .470 
i     -240 

.470 
.240 

1000 

39 

1000 

39 

IOOO 

39 

IOOO 

i 

IOOO 
21 

}      0.039 
}         -039 
}         -039 

>             .001 
>             .021 

|  ....Do  

J....DO  

Slow  evaporation; 
no  influx 

NUCLEI    OF    PURE    WATER. 


5.  Rapid  evaporation  of  fog  particles.  Vapor  nuclei. — Finally,  the 
fog  particle  precipitated  on  vapor  nuclei  may  be  rapidly  evaporated  by 
compression  (influx  of  air).  In  order  that  all  results  may  be  comparable, 
it  is  necessary  to  allow  the  same  time  interval  between  the  first  ex- 
haustion (capture  of  vapor  nuclei)  and  the  second  (capture  of  residual 
water  nuclei).  Since  filtered  air  enters  in  the  same  way  here  as  in  the 
foregoing  section  4,  its  effect  (if  any)  is  eliminated  from  the  results.  Sub- 
sidence, however,  is  essentially  reduced  by  the  present  method,  since  the 
time  for  subsidence  is  but  one-third  to  one-fifth  as  large  as  in  section  4. 
The  results  are  given  in  table  4  on  the  same  plan  as  in  table  3 .  In  part  i 
two  control  experiments  with  gradual  exhaustions  are  introduced  to 
indicate  the  difference.  The  nucleations  are  as  a  rule  low.  In  part  2  they 
are  high  and  there  is  one  control  experiment.  The  curve  is  shown  in  Nos. 
6  and  7  in  fig.  i. 

The  data  taken  from  smoothed  curves  will  therefore  be  about  as 
follows,  d  being  the  approximate  diameter  of  fog  particles,  subsidence 
being  ignored  and  the  exhaustion  loss  0.25. 


Number  of 

Number  of 

io«d 

io~3n 

n'/n 

Complete 
evaporation. 

nuclei 
evaporating 

residual 
nuclei 

(rcXio-3). 

(wXio-3). 

cm. 

16 

1500 

.... 

.... 

.... 

.... 

19 

1000 

0.039 

0.71 

710 

39 

20 

800 

.060 

.69 

550 

48 

22 

600 

.082 

.67 

400 

49 

25 

400 

.105 

•65 

260 

42 

32 

200 

.126 

.62 

125 

25 

The  apparently  greater  persistence  of  water  nuclei  on  rapid  evapor- 
ation is  thus  sustained.  Subsidence  is  in  excess  in  section  4 ;  and  though 
of  the  same  order  as  the  number  of  persistent  nuclei,  it  always  refers  to 
the  total  charge  of  nuclei.  As  the  number  to  be  accounted  for  in  the 
present  instance  can  not  well  be  estimated,  it  is  safe  to  conclude  that 
about  95  per  cent  of  the  fog  particles  precipitated  on  vapor  nuclei  evapo- 
rate without  residue,  when  about  io6fog  particles  are  suspended  in  each 
cubic  centimeter ;  and  that  this  percentage  decreases  with  the  number  of 
fog  particles  or  vapor  nuclei  caught,  or  as  their  size  increases.  Conversely 
the  number  of  residual  water  nuclei  persistent  within  5  minutes  increases 
as  the  number  of  fog  particles  decreases  (i.  e.,  as  their  size  increases)  from 
a  persistence  of  about  0.054  at  w=io6  to  over  0.17  at  w=2Xio5.  One 
would  thus  be  tempted  to  conclude  that  larger  fog  particles  take  a  longer 
time  to  evaporate  completely ;  but  that  the  case  is  far  more  subtle  will 
appear  in  the  next  paragraph. 


8  CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

6.  Evaporation  retarded  as  the  diameter  of  fog  particles  decreases. — 

A  suggestive  inference  may  be  drawn  from  the  results  obtained.  The 
visible  part  of  the  fog  vanishes  within  less  than  a  minute  after  the  com- 
pression, or  the  (necessarily  slow)  influx  of  dust-free  air  begins.  Here, 
then,  by  far  the  greater  bulk  of  the  particle  vanishes.  In  the  ensuing  5 
minutes  or  more,  optically  quite  inappreciable  water  nuclei  are  still 
present,  to  the  extent  of  5  to  20  per  cent  of  the  original  charge  of  vapor 
nuclei.  In  other  words,  whereas  the  tendency  to  evaporate  increases 
rapidly  with  the  diameter  of  the  fog  particle,  there  must  be,  in  case  of  the 
fog  particles  in  question,  some  counteracting  tendency  in  action,  by 
which  this  evaporation  is  retarded  much  in  excess  of  the  accelerating 
effect  of  convexity.  All  this  occurs  in  rigorously  dust-free  air,  in  which 
water  vapor  and  the  ions  (less  than  i  ,000  per  cubic  centimeter,  whereas 
there  are  from  25,000  to  50,000  water  nuclei)  inseparable  from  air  and 
due  to  natural  causes,  are  alone  present.  It  therefore  becomes  interesting 
to  endeavor  to  ascertain  the  reason  of  this  complete  inversion  of  the 
behavior  usually  characteristic  of  these  exceptionally  small  droplets. 

7.  Time  losses. — The  effect  of  lapse  of  time  between  the  exhaustions 
has  already  been  shown  to  be  of  minor  importance  within  intervals  like 
those  of  the  above  observations.      It  is  important,  however,   to  add 
quantitative  work,  and  table  5  supplies  relevant  data,  dp  being  the  drop 
of  pressure  on  exhaustion,  n  the  nucleation,  nf  /n  the  ratio  of  successive 
nucleations.    Table  5  shows  that  the  nucleation  is  spontaneously  reduced 
by  diffusion  to  about  one-half,  in  the  interval  between  the  second  and 
tenth  minutes,  and  so  far  as  may  be  observed  the  decrease  is  fairly 
uniform.     One  may  therefore  estimate  a  time  loss  of  about  6  per  cent 
per  minute.     Consequently   the  coronas  obtained  in  the   second  and 
third  minutes  (or  even  later)  are  liable  to  show  no  discernible  difference 
comparable  with  the  other  possible  complications  involved.     Thus,  for 
instance,  the  loss  of  water  nuclei  proper  can  not  begin  before  all  the  fog 
particles  have  evaporated,  a  process  which  must  consume  a  minute  at 
least  if  an  influx  of  strictly  dust-free  air  is  to  be  assured. 

Table  5  also  gives  evidence  to  the  effect  that  no  nuclei  come  through 
the  filter.  If  the  partial  vacuum  is  gradually  raised  to  dp  =  36  cm.  without 
sudden  exhaustion,  i.  e.,  without  initial  coronas,  and  filtered  air  is  then 
passed  in  the  identical  way  through  the  filter  into  the  fog  chamber,  no 
water  nuclei  whatever  are  detected  by  the  sudden  exhaustion  at  dp  =  1 8 
cm.  This  is  conclusive  proof  that  the  evaporation  of  fog  particles  is  the 
sole  cause  of  nucleation. 

Again,  table  5  shows  that  by  keeping  the  influx  cock  open,  nearly  9 
per  cent  of  the  fog  particles  may  be  represented  by  water  nuclei  even 
when  M=io6.  It  is  not  safe  to  admit  a  more  rapid  influx  at  the  filter, 
but  the  sudden  introduction  of  previously  filtered  air  suggests  itself  as  a 
means  to  the  same  end,  and  will  be  tried  in  turn. 


NUCLEI    OF    PURE    WATER. 


TABLE  5. — Water  nuclei  from  evaporation  of  fog  particles  precipitated  on  vapor  nuclei 
in  dust-free  air.    Effect  of  lapse  of  time  and  of  drop  of  pressure. 


Time 

elapsed 
between 
exhaus- 
tions 

» 

Corona. 

s 

Fog 
dissipated 
by— 

dp/p 

«J 

Ratio 

n'/n 

(minutes). 

Part  i.  —  Effect  of  lapse  of  time  between  exhaustions.     Barometer  75.26  at  26°. 

<?/>=•  36  and  dp=iS  or  dp/p  =  0.475  and  0.245. 

2m        / 

g 
rg 

72 



IOOO 

86 

\  0.86 

3m       { 

.... 

g 
rg 

72 

.... 

IOOO 

86 

}      .86 

_m        J 

g 

.... 

IOOO 

1 

5          | 

70 

Slightly 

.... 

79 

J      •  79 

10*         I 



g 

56" 

open  influx 
cock. 

IOOO 

40 

|      .40 

2m        / 

:::: 

g 

72 

.... 

IOOO 

86 

}      .86 

5m        { 

.... 

g 

66 

.... 

IOOO 

65 

}  * 

m         / 

g 

IOOO 

\ 

{ 

.... 

55 



37 

1     '37 

2m         | 

none 

f       

o 

|    

.... 

none 

o 

.... 

1       .... 

o 

/   .... 

Part  2.  —  Effect  of  different  drops  of  pressure  dp.     Barometer  75.26  at  26°. 

2m        | 

36.0 

g 

f    0.475 

IOOO 

19.9 

72 

.265 

90 

.... 

2m          | 

36.0 

21.6 

g 

72 

Slightly 
open  influx 
cock. 

•475 
.290 

IOOO 

98 

:::: 

om        J 

36.0 

g 

.  .  .  .' 

•475 

IOOO 

.... 

27.0 

60 

I       -360 

66 

.... 

Part  3.  —  Very  rapid  evaporation   (0.25   minute).     Barometer   76.22   at   24°. 

i-5m     { 

36.0 
20.  o 

gbp 

80 

Rapid 

IOOO 

123 

J  0.123 

i-5m     { 

36.0 

20.0 

v  b  p 

80  " 

influx  from 
tank  of 
dust-free 

.... 

IOOO 

145 

}     .US 

m     / 

36.0 

g 

.... 

air. 

IOOO 

I 

1 

20.  o 

!gbp 

80 

123 

/ 

10        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


TABLE  5. — Water  nuclei  from  evaporation  of  fog  particles  precipitated  on  vapor  nuclei 

in  dust-free  air — Continued. 


Time 

elapsed 
between 
exhaus- 
tions 

dp 

Corona. 

s 

Fog 
dissipated 
by- 

dp/p 

— 

Ratio 

n'/n 

(minutes)  . 

Part  4.  —  Larger  particles.     Rapid  evaporation   (less  than  0.25  minute).     Baro- 

meter 76.69  at  23°. 

i-5m     { 

29.8 
17-3 

y° 

r  b  p 

8.0 

0.388 
.225 

540 
1  08 

>    0.20 

r 

29.8 

y  o 



.388 

540 

\ 

x-5m     | 

17.3 

r  b  p 

7-7 

.225 

97 

J      <J 

r 

28.0 

c 

9.0 

Influx  of 

.365 

290 

\ 

I-5m     | 

17-3 

yb 

8.0 

filtered 

.225 

108 

J 

t 

28.0 

r 

9-5 

air  from 

•365 

260 

•> 

i-5m     ( 

17-3 

g  !bp 

7-7 

reservoir. 

.225 

97 

J      <37 

r 

26.2 

corona 

5-7 

•342 

54 

"I 

i.5        ( 

17-3 

4.2 

.225 

16 

J      '3° 

i    ^m     < 

27.0 

corona 

7.6 

•352 

130 

)    ^ 

1 

17-3 

.... 

5-4 

.225 

33 

! 

*A11  conditions  identical  to  the  above,  except  that  there  is  no  primary  exhaustion  or  fog  precipitation 
on  vapor  nuclei.     The  absence  of  all  condensation  at  18  shows  that  no  nuclei  come  through  the  filter. 

8.  Effect  of  changes  of  the  drop  of  pressure  dp. — The  second  part  of 
table  5  contains  results  in  which  residual  water  nuclei  are  captured  at 
drops  of  pressure  from  dp=iS  to  27  cm.  At  first  the  coronas  do  not 
change ;  eventually  they  decrease  in  a  way  to  be  referred  to  the  increased 
amount  of  water  precipitated.  Vapor  nuclei  are  inefficient  in  the  presence 
of  water  nuclei. 

The  constancy  of  coronas  after  all  nuclei  have  been  caught  through  a 
considerable  range  of  values  of  dp,  occurs  here  as  elsewhere  and  has  not 
yet  been  fully  explained.  As  the  nucleation  n  varies  with  the  precipi- 
tation (m  grams  per  cu.  cm.),  while  n  increases  with  dp,  the  computed 
values  of  n  must  also  do  so,  thus  conflicting  with  the  observed  fixed 
coronal  aperture.  It  is  difficult  to  conjecture  where  the  excess  of  water 
precipitated  goes  to,  even  if  we  recall  the  slow  change  of  5  implied  in 
dct^/m  or  s$/m  =  const.  In  some  way,  probably  coincident  with  the  rise 
of  temperature  after  adiabatic  cooling,  the  excess  of  precipitation  is  again 
removed  before  coronas  can  be  observed.  The  efficiency  of  the  fog 
chamber  virtually  breaks  down,  as  no  more  water  is  deposited  when  dp 
increases. 

It  follows  in  general  that  neither  by  the  time  loss  nor  by  the  effect  of  a 
varying  drop  of  pressure  is  the  tendency  of  rapid  evaporation  to  produce 
persistent  water  nuclei  materially  influenced.  It  must,  therefore,  be  an 
occurrence  of  its  own  kind. 


NUCLEI    OF    PURE    WATER. 


II 


9.  Exceptionally  rapid  evaporation. — In  the  third  and  fourth  parts 
of  table  5  the  influx  of  dust-free  air  was  increased  in  a  marked  degree, 
by  withdrawing  the  influx  of  dust-free  air  from  a  large  independent 
reservoir.  In  this  way  the  time  of  evaporation  was  reduced  to  about  1 5 
seconds.  Nevertheless  it  required  about  1.5  minutes  to  reduce  the  pres- 
sure from  dp  =  36  cm.,  to  dp  =  20  cm.,  so  that  some  water  nuclei  vanished 
by  decay.  The  yield  of  water  nuclei  has  been  materially  increased.  Thus 
even  when  w=io8  or  d  =  o. 00019  cm.,  rapid  evaporation  will  convert  at 
least  1 8  per  cent  of  the  fog  particles  of  pure  water  into  persistent  water 
nuclei.  The  case  is  most  pronounced  for  n  =  300,000  to  400,000  nuclei 
per  cubic  centimeter,  or  d  =  0.0002 7  cm.,  when  48  per  cent  of  the  nuclei 
(about  one-half),  persist.  Beyond  this,  n  =  io5,  the  persistence  decreases, 
a  result  doubtless  referable  to  the  increasing  importance  of  subsidence. 
Within  reasonable  limits  persistence  increases  as  the  original  number 
of  nuclei  decreases,  which  result  is  identical  with  the  character  of  the 
earlier  series. 

Naturally  all  these  data  are  lower  limits.  In  appropriate  apparatus 
the  time  of  evaporation,  the  interval  of  observation,  etc.,  might  be  made 
much  shorter;  but  this  would  not  change  the  general  trend  of  the  data. 
Again,  many  particles  must  be  washed  out  by  contact  with  the  sides  of 
the  vessel  or  by  coalescence,  during  the  turbulent  motion  which  accom- 
panies the  influx  of  air.  The  following  is  a  digest  of  the  data  found: 


Ratio 

Corrected 

dXio8 

wXio-3 

Exhaus- 
tion loss. 

Subsid- 
ence loss. 

Evapora- 
tion loss. 

Residual 
water 
nuclei. 

residual 
water 
nuclei  to 
total  water 

number  of 
residual 
water 
nuclei 

nuclei. 

(nXio-3). 

cm. 

190 

IOOO 

0.23 

0 

0.64 

0.13 

0.17 

170 

240 

500 

•23 

o 

•58 

.19 

•25 

125 

270 

350 

•23 

o 

.40 

•37 

.48 

168 

410 

100 

•23 

0 

•49 

.28 

.36 

36 

10.  Conclusion. — For  very  small  fog  particles  suspended  in  dust-free 
air  saturated  with  water  vapor  and  left  without  interference,  the  dis- 
sipation by  evaporation  is  enormously  more  important  than  that  by 
subsidence.  In  the  above  plug-cock  fog  chambers  the  transition  occurs 
when  the  number  of  nuclei  per  cubic  centimeter,  n  =  200,000,  or  the 
diameter  of  fog  particles,  d  =  0.0003  cm->  when  about  half  evaporate  and 
half  subside. 

Fog  particles  precipitated  on  solutional  nuclei  (phosphorus) ,  evaporate 
to  persistent  water  nuclei  without  other  loss  than  is  attributable  to  sub- 
sidence and  in  a  small  degree  to  time  losses  (diffusion) .  There  is  no  loss 
by  complete  evaporation. 


12        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

Fog  particles  precipitated  on  the  nuclei  of  water  vapor  in  dust-free  air, 
in  contrast  with  the  preceding  case,  evaporate  under  the  same  circum- 
stances almost  without  residue,  the  yield  of  water  nuclei  (after  allowing 
for  subsidence  and  in  the  absence  of  all  interference)  being  but  0.004 
when  d  =  0.00016  cm.,  increasing  to  0.0036  when  d  =  0.0003 2  cm-  These 
fog  particles  evaporate  into  the  wet  air  from  which  they  were  precipi- 
tated, and  the  experiment  may  be  repeated  indefinitely.  Relatively  more 
water  nuclei  persist  as  the  fog  particles  evaporated  are  larger. 

11.  The  same,  continued. — The  persistence  of  water  nuclei  obtained 
in  the  last  case  from  the  nuclei  of  water  vapor  is  much  increased  by 
accelerating  the  evaporation  of  the  fog  as  soon  as  formed.  Such  forced 
evaporation  is  produced  by  the  rise  of  temperature  due  to  the  com- 
pression accompanying  the  influx  of  dust-free  air  after  the  exhaustion 
which  precipitated  the  fog.  This  result  can  not  be  associated  with  losses 
due  to  subsidence. 

When  the  rate  of  evaporation  is  increased  by  compression,  moreover, 
the  number  of  water  nuclei  (derived  from  the  reasonably  rapid  evapor- 
ation of  fog  particles  precipitated  on  vapor  nuclei  and  persisting  within 
5  minutes  after  the  evaporation)  may  be  as  large  as  5  per  cent  to  over  20 
per  cent,  depending  upon  the  size  (d=igXio~5  to  d  =  32Xio~5  cm., 
respectively)  of  the  fog  particles  evaporated.  Again,  relatively  more 
water  nuclei  persist  when  the  fog  particles  evaporated  are  larger  within 
limits  given.  By  keeping  the  influx  cock  for  dust-free  air  slightly  open 
on  sudden  exhaustion,  10  per  cent  of  the  fog  particles  evaporated  may  be 
represented  by  persistent  water  nuclei,  even  when  d  =  1 9  X  i o~5  cm.  or  n  = 
io6.  If  it  were  safe*  to  make  use  of  more  rapid  evaporations,  this  limit 
could  unquestionably  be  much  increased.  Thus  on  the  rapid  evaporation 
of  fog  particles  by  the  influx  of  filtered  air  from  a  large  independent  reser- 
voir into  the  fog  chamber,  about  18  per  cent  of  the  fog  particles  were 
converted  into  residual  water  nuclei  when  n—  io8  and  actually  48  per  cent 
when  n=io5.  All  such  values  or  lower  limits,  because  the  loss  of  fog 
particles  at  the  walls  of  the  vessel  and  by  coalescence  is  not  included, 
but  tests  under  most  rapid  evaporation  possible  showed  that  a  limit  had 
been  practically  reached. 

The  loss  of  nuclei  by  decay  (diffusion)  in  the  lapse  of  time  (say  6  per 
cent  per  minute  within  the  given  interval  of  observation)  and  the  effect  of 
changes  in  the  drop  of  pressure  on  sudden  exhaustions  have  no  causal 
bearing  on  the  production  of  water  nuclei  by  rapid  evaporation.  They 
merely  modify  the  number.  Similarly  the  effect  of  subsidence  is  second- 
ary. Hence  the  cause  of  the  production  of  persistent  water  nuclei  in 
rigorously  dust-free  air  must  be  associated  with  the  speed  of  evaporation 
or  with  the  motion  of  the  fog  particles  during  evaporation.  It  is  a  curious 

*  Naturally  the  efficiency  of  the  filter  must  be  tested  before  each  experiment. 


NUCLEI  OF  PURE  WATER.  13 

fact  that  whereas  the  relatively  enormous  fog  particle  evaporates  at  once 
beyond  the  range  of  visibility,  this  process  stops  in  case  of  certain  of  the 
invisible  particles  making  about  0.5  to  50  per  cent  of  the  total  number 
as  the  evaporation  is  more  rapid  in  the  manner  specified.  The  remaining 
fog  particles  evaporate  completely. 

12.  The  same,  continued. — J.  J.  Thomson,  Langevin  and  Bloch,  and 
others*  have  referred  the  persistence  of  pure  water  nuclei  of  about  io~6 
cm.  in  diameter,  to  the  minimum  of  surface  tension  discovered  by  Reinold 
and  Riickerf  for  thicknesses  of  films  of  about  the  same  value.    Since  all 
fog  particles  are  so  much  larger  than  this  order  of  values,  it  is  difficult  to 
see  why,  under  quiet  evaporation  without  any  interference,  they  do  not 
all  terminate  in  water  nuclei,  allowance  being  made  for  subsidence.    Yet 
under  these  circumstances  the  yield  of  water  nuclei  is  least,  being  usually 
within  i  per  cent.     Whatever  losses  may  be  due  to  coalescence  should 
be  increased  when  the  rate  of  evaporation  is  increased,  because  there  is 
more  motion  of  the  air  relatively  to  the  fog  particles.     Again,  precisely 
the  reverse  occurs,  inasmuch  as  an  increased  rate  of  evaporation  enor- 
mously increases  the  yield  of  water  nuclei. 

Moreover,  the  residual  water  nuclei  may,  on  rapid  evaporation,  exceed 
the  order  of  io~6  cm.  in  diameter  two  or  three  times;  or  on  slow  evapor- 
ation they  may  fall  below  5Xio~7  cm.  and  yet  persist  for  half  an  hour 
or  more.  Under  any  circumstances  they  are  graded.  They  appear  to 
diminish  in  size  with  extreme  slowness  in  the  lapse  of  time,  so  that  an 
appropriate  interval  of  waiting  will  yield  any  size. 

13.  The  same,  continued. — Since  the  fog  particles  are  absolutely  pure 
water  (water  condensed  on  water  vapor) ,  it  is  tempting  to  suggest  electri- 
cal charge  as  the  cause  of  the  observed  persistence,  such  charge  being 
acquired  either  by  friction  during  the  motion  of  particles  undergoing 
rapid  evaporation  (influx  of  air)  or  by  the  mere  act  of  evaporation.    The 
latter,  like  the  minimum  of  surface  tension,  would  require  the  same 
persistence  of  all  fog  particles  under  conditions  of  quiet  evaporation.    As 
has  frequently  been  shown,  this  is  not  the  case.    A  frictional  mechanism, 
suggested  in  view  of  the  occurrence  of  convection  during  the  period  of 
evaporation  and  influx  of  air,  if  in  action,  would  account  for  the  discrimi- 
nation between  fog  particles  as  to  survival.    Thus  drops  of  larger  size  are 
stirred  about  for  a  longer  time  before  complete  evaporation,  and  they  are 
therefore  more  favorably  circumstanced  to  persist,  as  they  have  been 
found  to  do ;  water  nuclei  should  not  be  of  the  same  size  and  they  are  not ; 
etc.    But  all  my  experiments  have  failed  to  detect  the  amount  of  charge 
commensurate  with  the  persistence  of  nuclei. 

*J.  J.  Thomson:  Conduction  of  Electricity  through  Gases,  p.  152,  1903;    C.  T.  R. 
Wilson,  Trans.  St.  Louis  Electrical  Congress,  vol.  i,  pp.  364-378,  1904. 
fReinold  and  Riicker:   Proc.  Roy.  Soc.,  vol.  40,  p.  441,  1886. 


14       CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

If  the  radius  of  residual  water  nuclei  be  taken  as  io~6  cm.,  the  charge 
needed  would  be  roughly  e  =  6.3  X  io~8 electro-static  units  per  particle  and 
its  potential  would  be  about  18  volts.  If  about  200,000  of  these  droplets 
or  residual  water  nuclei  are  present  per  cubic  centimeter  (as  were  found 
above),  the  charge  would  be  about  4  coulombs  for  a  cube  each  side  of 
which  is  100  meters.  If  all  the  particles  of  the  cubic  centimeter  were 
brought  to  coalescence  the  size  of  the  drop  would  be  58  X  io~6  cm.  at  its 
potential  of  about  63,000  volts.  Finally,  the  electric  contents  of  my  fog 
chamber  should  be  about  30  electro-static  units  of  quantity,  and  ought 
thus,  in  spite  of  the  moisture  present,  to  be  easily  determinable.  The 
experiments  showed  only  about  o.5oX  io~6  electro-static  units  per  cubic 
centimeter,  less  than  the  contents  (o.88X  io~6)  in  the  room  air  without, 
at  the  time;  that  is,  the  average  charge  per  nucleus  was  about  5X  io~12 
electro-static  units,  or  less  than  i  electron.  Hence  the  electrical  hypoth- 
esis must  be  abandoned.  It  would  in  any  case  be  improbable  for  the 
charge  to  show  so  small  a  coefficient  of  decay  as  do  the  water  nuclei. 

14.  Statistical  hypothesis. — Under  the  circumstances  it  seems  per- 
missible to  suggest  an  hypothesis  of  a  statistical  character;  namely,  that 
the  molecule  of  liquid  water  is  composite,  consisting  of  virtually  more 
volatile  and  less  volatile  constituents.  Such  a  view  is  quite  compatible 
with  the  composite  molecule  observed  in  water  vapor,  where  millions  of 
nuclei  may  be  captured  long  before  the  molecule  proper  is  reached,  the 
evidences  of  which  are  now  beyond  question.  In  case  of  fog  particles, 
when  the  evaporation  is  reduced  to  extreme  slowness,  we  may  conceive 
that  all  groups  of  molecules  evaporate  together  at  about  the  same  rate, 
and  that  therefore  the  residue,  i.  e. ,  the  persistent  water  nuclei,  are  present 
in  least  amount.  On  the  other  hand,  when  the  evaporation  is  forced,  or 
accelerated  by  the  heat  due  to  compression,  the  more  volatile  constituents 
of  the  fog  particles  evaporate  faster  than  the  less  volatile,  and  there  is  a 
correspondingly  greater  residue  of  persistent  water  nuclei,  because  of  this 
concentration  of  the  less  volatile  molecular  aggregates  of  water  in  each 
fog  particle.  It  follows  also  that  relatively  more  persistent  nuclei  are 
obtained  by  the  evaporation  of  large  fog  particles  than  by  the  evaporation 
of  small  particles,  because  a  greater  relative  number  of  these  droplets 
would  contain  a  sufficient  number  of  the  less  volatile  groups  to  persist; 
i.  e.,  the  opportunities  for  concentrating  the  less  volatile  aggregates  are 
enhanced.  Finally,  it  should  never  be  possible  to  replace  all  fog  particles 
by  the  water  nuclei  derived  from  them.  All  of  these  deductions  are  in 
keeping  with  the  experimental  evidence,  as  pointed  out. 


CHAPTER  II. 

STANDARDIZATION  AND  EFFICIENCY  OF  THE  FOG  CHAMBER. 
AXIAL  COLORS  AND  INTERFERENCES. 

15.  Introductory. — The  axial  colors  of  the  steam  jet  and  of  coronas 
overlie  the  source  of  light  when  looked  at  through  a  long  column  of  wet 
air  in  which  uniform  cloud  particles  are  suspended.     It  makes  no  differ- 
ence whether  the  source  is  a  point  simply  or  a  disk  (say)  4  inches  in 
diameter;  it  appears  uniformly  colored,  as  if  seen  through  colored  glass, 
so  long  as  the  cloud  lasts.    The  order  of  colors,  beginning  with  particles 
of  extreme  smallness,  is  the  same  as  that  of  Newton's  interferences  seen 
by  transmitted  light.     In  case  of  the  steam  jet,  however,  on  passing  the 
transition  from  crimson  to  violet  in  the  first  order,  the  field  becomes 
opaque,  while  the  steady  flow  of  the  jet  usually  breaks  down  and  becomes 
turbulent.     In  the  case  of  coronas  I  have  thus  far  failed  to  reach  this 
transition,  the  medium  showing  mere  fogs  of  uncertain  character. 

To  produce  the  actual  colors  vividly,  and  especially  the  tints  of  the 
second  and  third  orders  for  relatively  large  particles,  the  columns  of  fog 
must  be  long  and  very  uniform.  The  steam  jet  soon  fails  in  this  respect, 
but  a  wide  drum  i  to  2  meters  long  used  as  a  fog  chamber  shows  saturated 
colors  surrounded  by  coronas.  In  the  case  of  hydrocarbon  vapors  the 
columns  may  be  shorter,  because  the  particles  throughout  are  larger  for 
like  numbers  per  cubic  centimeter  than  is  the  case  with  water  vapor. 

16.  Causes  of  axial  color. — In  my  earlier  work*  I   was   inclined   to 
regard  these  colors  as  interferences  superimposed  on  the  coronas,  regard- 
ing the  small  field  of  refraction  possible  with  small  particles  as  in  keeping 
with  the  long  columns  needed  for  observation.    The  explanation  at  best 
is  purely  tentative.    Later  in  my  work,  when  the  size  of  particles  was  esti- 
mated from  data  given  by  successive  exhaustions,  f  it  appeared  that  the 
sizes  of  the  fog  particles  were  of  an  order  about  ten  times  larger  than  would 
be  needed  to  produce  interferences  of  the  same  kind.    The  interference 
hypothesis  was  therefore  abandoned.      In  my  more  recent  results  the 
diameter  of  fog  particles  d  and  the  ratio  in  question  are  somewhat  reduced 
but  remain  of  the  same  order.     Thus  if  n  be  the  number  of  fog  particles 
per  cubic  centimeter,  D  the  thickness  of  an  air  plate  giving  like  inter- 
ference colors,  the  results  given  in  table  6  may  be  selected  at  random. 
They  show  that  the  strong  axial  blues  of  the  first  order  must  belong  to 
particles  even  larger  than  o.oooi  cm.  in  diameter,  and  that  all  particles 
are  more  than  six  times  larger  than  would  be  demanded  for  interferences. 

*Phil.  Mag.  (5),  xxxv,  p.  315,  1893;  Bull.  U.  S.  Weather  Bureau  No.  12,  1895. 
fPhil.  Mag.  (6),  iv,  p.  26,  1902;  Smiths.  Contrib.  No.  1373,  1903;  No.  1651,  1905. 


l6        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AHD    IONS. 


6. — Data  for  axial  colors,    m  =  3.6  X  io~6  grams ;  V  ^  =  i  .90  X  io~2. 


DXio6 

Corona. 

Axial. 

s 

dXio5 

(fXio5 

wXio-3 

computed. 

Ratio 
d/D. 

14 

V 

36 

I  7 

b 

27 

gy 



46 





29 

•2-7 

bg 

y 

14-5 

22 

47 

650 

22 

7-7 

£•2 

41 

gy 

p 

13.0 

25 

55 

460 

25 

6.1 

42 

y 

V 

12.  0 

27 

60 

360 

26 

6.4 

45 

b 

II  .O 

29 

65 

280 

29 

6-5 

55 

p 

g 

10.  0 

32 

67 

213 

32 

5-8 

57 

y 

9.0 

36 

70 

152 

36 

6-3 

69 

gy 

V 

8.0 

40 

79 

1  08 

40 

5-8 

17.  The  lamellar  grating.  —  Recently  I  have  considered  the  case  of 
coronas  in  relation  to  the  lamellar  grating,  in  which  diffractions  are 
obtained  from  a  uniform  succession  of  alternately  different  thicknesses 
of  clear  glass.  Experiments  with  such  gratings  were  originally  made 
by  Quincke  and  there  is  a  full  theoretical  treatment  by  Verdet.  The 
behavior  of  this  grating  differs  from  that  of  the  usual  kind  in  the  occur- 
rence of  an  additional  factor 

cos2(nd(n  —  i)  -f  na  sin  $)/A 

where  n  is  the  index  of  refraction,  d  the  difference  in  thickness  between 
thin  strips  of  width  a  and  thick  strips  of  width  b,  d  the  angle  of  dif- 
fraction. Hence  since  for  axial  color,  d  =  o,  minima  occur  at  (n—i)d  = 
(2m  +  i)  .A/2,  whereas  for  Newton's  interferences,  the  mimima  occur  for 
a  thickness  D  in  the  case  of  transmitted  light  where  2fiD  =  (2W+  i)  .  A/2  ; 
whence 


n—  i 


In  case  of  water  n  =  0.133,  or  d/D  =  &.o.  This  result  applied  to  a  grating 
of  transparent  strips  is  so  near  the  above  datum  d/D  >  6  for  a  medium 
of  transparent  particles  (for  which  there  is  no  theory),  that  it  seems 
reasonable  to  conclude  that  the  actual  colors  are  referable  to  the  same 
type  of  phenomenon  in  both  cases.  The  need  of  observations  through 
long  columns  in  case  of  fog  particles  suspended  in  air  is  additionally  con- 
firmative, since  the  contribution  of  color  due  to  one  particle  must  be 
exceedingly  small. 

18.  Disk  colors  of  coronas.  —  One  might  be  tempted  to  explain  the 
disk  colors  in  the  same  way,  for  in  case  of  deviation  d  from  the  axial  ray 

D/d=  (n—i)/2H-\-a  sin  d/2  dn 

But  here  there  are  several  insuperable  difficulties  which  refer  the  disk 
color  to  a  different  origin.  In  the  first  place,  they  are  much  more  intense 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER.  17 

than  the  axial  colors  and  are  seen  distinctly  through  very  small  thick- 
nesses of  fog;  disk  colors  are  apparently  abruptly  complementary  to  the 
axial  colors  and  there  is  certainly  no  continuous  transition;  finally,  there 
is  no  incident  light  of  the  requisite  obliquity. 

The  appearance  is,  therefore,  as  if,  corresponding  to  the  interferences 
by  transmission,  there  were  complementary  interference  by  reflection 
toward  the  source  of  light.  This  phenomenon  could  then  be  reversed  in 
direction  at  any  fog  particle  in  its  path,  and  thus  turned  again  toward 
the  observer.  But  apart  from  the  complementary  nature  of  disk  and 
axial  color,  no  other  evidence  bears  on  this  explanation.  Moreover,  any 
such  theory  must  account  for  the  intensity  of  disk  colors  in  general,  and 
in  particular  for  the  vividness  of  the  greens. 

19.  Experiments  with  long  tubes. — In  a  long  chamber  and  intense 
illumination  the  axial  colors  may  be  extended  over  a  considerable  area 
and  intensified  by  strong  illumination.  It  did  not  seem  improbable  that 
they  might  then  be  serviceable  for  spectroscopic  investigation,  in  which 
case  the  mean  wave-length  of  the  interference  bands  would  serve  for 
their  identification.  Thus  they  might  afford  a  means  of  further  investi- 
gating the  fog  phenomenon  at  a  degree  of  fineness  beyond  which  the 
coronas  cease  to  be  available.  Unexpected  difficulties  were,  however, 
encountered,  as  will  presently  appear,  and  the  endeavor  to  remove  them 
has  not  been  successful. 


aoocm.- 


FIG.  2. — Section   of  brass   tube   for   observing 
axial  color. 

Experiments  of  this  kind  were  begun  by  using  long  brass  tubes  (fig.  2) 
with  plate  glass  ends,  carefully  put  together.  Sometimes  wet  cloth  linings 
were  introduced;  but  they  had  no  other  effect  than  to  dispel  the  hori- 
zontal columnar  vortices  seen  on  each  side  of  the  axis  after  exhaustion. 
With  a  naked  tube  the  fog  observed  rises  on  the  outside  and  falls  in  the 
center  of  the  field,  so  that  the  axes  of  the  two  vortical  columns  are  eccen- 
trically placed  parallel  to  the  axis  of  the  tube.  Phosphorus  nuclei,  ions, 
and  vapor  nuclei  were  tried,  and  incidentally  some  fog  and  rain  limits 
determined. 

The  following  summary  of  results  with  vapor  nuclei  or  with  ions  (dp 
being  the  drop  in  pressure) ,  shows  that  in  no  case  was  there  any  color 
obtainable.  In  these  narrow  tubes  the  only  manifestation  is  a  more  or 
less  densely  black  fog. 


l8        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


TABLE  7.  — Observations  for  axial  color.    Dust-free  air,  vapor  nuclei,  and  ions.    Long 
brass  tube,  5  cm.  diameter,  200  cm.  long. 


dp 

Precipitate. 

dp 

Precipitate. 

dp 

Precipitate. 

Part  i  .  —  B  arometer  77.28 
at  18°. 

Part  3  .  —  B  arometer  77.34 
at  1  8°. 

Part  7.  —  Barometer  77.65 
at  20° 

21  .O 
22.6 
24.6 
26.3 
28.0 

Fog 
Fog 
Fog 
Fog 
Fog 

*i9.8 
19.4 
20.4 
20.9 

21  .O 

Just  seen 
None 
None 
Just  dim. 
Faint  fog 

*i8.o 
18.0 
19.4 
20.3 
21.3 
22.4 

Darkness 
Darkness  ! 
Darkness  ! 
Darkness  ! 
Rain 
Corona 

Part  2.  —  Barometer  77.37 
at  19°. 

Part  4.  —  Small  round  hole  ; 
sharper  seeing  ;  barom- 
eter 77.34. 

Part  8.  —  Barometer  77.65 
at  20°. 

15-4 
16.2 

*17'6 
*i9-4 

21.3 
20.4 
23.0 

24-5 
26.4 
28.0 
29.9 
31-6 
33-1 
35-o 

None 
None 
None 
None 
Light  fog 
None 
Fog 
Fogf 
Fogf 
Fogf 
Fogf 
Fogf 
Fogf 
Fogf 

•at.  i 

20.4 

Rain 
Rain,  faint 

21.4 
20.  6 
19.4 

18.5 

Corona 
Corona 

(?) 
Darkness 

Part  5.  —  Radium  on  tube, 
outside;   barometer  77.34. 

Part  9.  —  Radium  on  tube. 

*20-4 

19.4 

19-3 
20.3 

21  .  I 

Fog  dense 
Rain  ! 
Rain  ! 
Dense 
Fog 

18.0 
18.9 

19-5 
20.4 

24-3 
25-0 

(?) 
Rain  ? 
Corona  ! 
Corona  ! 
Dense 
Dense 

Part    6.  -Cloth    hung    in 
brass  tubes;   barometer 
76.24  at  21°. 

Part   i  o  —  Dust-free  air 
again.  J 

17.6 
19.2 

21.0 

23 
24 
26 
28 
30 

None 
Fog? 
Fog? 
Fog! 
Fog  ! 
Fog! 
Fog  ! 
Fog!  J 

24-5 
26.4 
28.0 
No  coloi 

Corona 
Corona 
Corona 
"  appears. 

*Fog  limits.  fDense  but  no  color.  JDense  fog  but  no  color. 

The  same  is  true  of  phosphorus  nuclei  put  into  the  identical  (now  cloth- 
lined)  apparatus.  Thus  in  case  of  long  brass  tubes  200  cm.  in  length  and 
5  cm.  in  diameter  with  the  barometer  at  77.15  cm.  at  20°,  thirteen  succes- 
sive exhaustions  of  air  charged  with  phosphorus  nuclei  showed  no  color 
effects,  but  merely  fogs  gradually  decreasing  in  density.  The  drop  of 
pressure  lay  between  10  and  16  cm. 

Again,  four  exhaustions  with  fresh  charges  of  phosphorus  nuclei  be- 
haved similarly.  The  nucleated  air  was  usually  fawn-colored  by  trans- 
mitted light  and  bluish  by  reflected  light.  Finally,  when  many  successive 
charges  of  phosphorus  nuclei  were  introduced,  densely  black  fogs  appeared 
without  color,  gradually  lifting. 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 


The  endeavor  to  clean  the  fog  chamber  by  successive  exhaustion  and 
apparently  complete  subsidence  failed  utterly.  Fog  particles  evaporate 
before  subsidence  to  persistent  water  nuclei,  so  that  for  small  particles 
(above  the  middle  green  corona),  subsidence  is  negligible  as  compared 
with  evaporation,  even  in  a  long  brass  channel  lined  with  a  square  tube 
of  wet  cloth  4  cm.  high  and  4  cm.  wide. 

20.  Short  tubes. — Believing  that  any  irregularity  in  the  size  of  the 
fog  particles  might  be  particularly  harmful  in  the  case  of  tubes  2  meters 
long,  short  tubes  of  the  same  diameter  were  next  tried  in  the  endeavor 
to  obtain  axial  color  effects  with  vapor  nuclei.  The  results  are  given  in 
table  8. 

TABLE  8.  — Observations  for  axial  color.  Dust-free  air.  Vapor  nuclei.  Short  brass 
tube,  5  cm.  diameter,  75  cm.  long.  Tube  not  cloth-lined.  Part  15.— Barometer  77.00 
at  21°. 


* 

Precipitate. 

** 

Precipitate. 

dp 

Precipitate. 

*i8.5 

Rain 

*2O.Q 

Corona 

35-7 

Dense 

*i8.o 

Rain 

21.6 

Corona 

40.6 

Dense 

*i?-5 

None 

23-4 

Corona 

43-i 

Dense 

*i7.o 

None 

25-3 

Corona 

46.6 

Dense 

*i8.o 

None 

f28.7 

Dense 

*i9.9 

None 

32 

Dense 

"The  difference  of  fog  limit  or  rain  limit  for  descending  and  ascending  dp  is  noteworthy. 
fNo  colors  seen.     Subsidence  with  a  horizontal  plane  on  top. 

The  attempt  again  failed.  No  colors  were  observed,  merely  an  evenly 
subsiding,  gradually  (increasing  dp)  more  intensely  black  fog. 

These  results  are  disappointing.  To  obtain  axial  colors  (coronas  are 
not  observable  longitudinally  in  tubes) ;  it  therefore  seems  essential  that 
drums  of  considerable  equatorial  diameter  be  used.  In  other  words,  the 
vessel  must  not  only  be  long  but  voluminous  to  obviate  the  radiation 
effect  from  the  walls  after  exhaustion,  as  much  as  possible.  In  fact,  the 
external  layers  of  foggy  air  seem  effectually  to  screen  the  interior  from 
the  radiation. 

Incidentally  a  number  of  fog  limits  and  rain  limits  were  obtained, 
which,  however,  present  nothing  new,  except  that  on  diminishing  pressure 
differences  dp,  the  rain  limit  falls  at  a  lower  dp  than  on  ascending  differ- 
ences. The  appearance  is  as  if  the  fine  droplets  generated  nuclei.  But 
more  probably  very  fine  nuclei  escape  capture  in  the  presence  of  coarse. 

Summarizing  the  above  results,  we  may  therefore  conclude  that  the  fog 
particles  producing  the  axial  colors  of  coronas  are  of  such  a  size  as  to 
recall  the  interference  phenomena  of  the  lamellar  grating,  with  which 
their  constants  agree. 

The  disk  colors  of  coronas  can  not  be  similarly  explained. 

The  observation  of  axial  color  fails  unless  long,  capacious  fog  chambers 
are  used.  Tubes  show  opaque  fields  only. 


20        CONDENSATION    OF    VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 
CORONAS  WITH  MERCURY  LIGHT. 

21.  Preliminary  survey.— The  inferences  of  the  preceding  papers* 
gave  the  promise  that  on  judiciously  using  monochromatic  light  as  the 
source  of  illumination  the  optical  nature  of  the  coronas  might  be  fully 
brought  out.  Such  light  must  be  strictly  homogeneous  and  at  the  same 
time  very  intense.  Hence  the  usual  methods  of  obtaining  it  are  unsatis- 
factory. The  strong  green  line  of  a  mercury  lamp,  however,  fulfills  the 
requirements  admirably,  and  this  was  therefore  used.  The  results  show 
that  the  green  disk  and  the  first  green  ring  alternately  vanish  as  the  result 
of  the  interference  phenomenon  superimposed  on  the  diffraction  phe- 
nomenon. If,  therefore,  the  nucleation  of  a  highly  charged  medium  is  sys- 
tematically reduced,  a  series  of  angular  diameters  may  be  obtained,  both 
for  the  green  disk  and  the  inner  or  outer  edge  of  the  first  green  ring. 
From  the  loci  of  these  values  the  position  of  the  first  diffraction  mini- 
mum for  green  light  may  be  inferred,  and  the  size  of  droplets  computed 
from  the  usual  equation  for  small  opaque  particles. 

If  the  reduction  of  the  nucleation  is  accomplished  by  successive  partial 
exhaustions,  all  of  them  identical,  while  filtered  air  is  allowed  to  enter 
the  receiver  systematically  between  the  exhaustions,  the  nucleations  of 
any  two  consecutive  exhaustions  should  show  a  constant  ratio.  Allow- 
ance must,  however,  be  made  for  the  subsidence  during  the  later  fogs  and 
for  time  losses,  if  any.  This  is  the  method  used  hitherto  in  my  work  and 
the  results  seem  to  have  been  trustworthy. 

In  the  case  of  mercury  light,  however,  it  is  now  possible  to  compare 
the  latter  with  the  former  (diffraction)  method  of  obtaining  the  diameter 
of  particles,  with  a  view  to  throwing  definite  light  on  the  optical  phenome- 
non. Subsidence  methods  are  out  of  the  question  for  large  coronas,  as 
these  are  invariably  fleeting  in  character  and  pass  at  once  into  smaller 
coarse  coronas. 

The  results  of  the  two  methods  may  be  regarded  as  coincident  as  long 
as  not  more  than  300,000  nuclei  per  cubic  centimeter,  or  diameters  of 
particles  not  smaller  than  0.0003  cm.  are  in  question.  For  larger  numbers 
and  smaller  diameters  the  divergence  rapidly  increases.  Indeed,  for 
particles  larger  than  the  size  given,  the  optically  measured  loss  per 
exhaustion  exceeds  the  exhaustion  ratio,  a  result  which  is  satisfactorily 
explained  by  the  contemporaneous  subsidence  of  these  relatively  large 
particles.  For  particles  smaller  than  the  limit  in  question,  however,  the 
loss  computed  by  the  optic  method  is  larger  than  the  exhaustion  loss,  as 
if  fresh  nuclei  were  produced  or  rather  made  available  at  each  exhaustion. 
It  is  this  result  which  the  present  paper  purposes  to  bring  out  in  detail 
and  to  consider  in  its  bearings  on  the  optical  phenomenon. 

*Amer.  Journ.  Sci.,  xxv,  1908,  p.  224;  xxvi,  1908,  p.  87;  xxvi,  1908,  p.  324. 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER.  21 

22.  Apparatus.  —  The  fog  chamber  was  of  the  usual  pattern,  cylin- 
drical in  form,  with  its  axis  horizontal.  The  clear  walls,  being  of  blown 
glass,  showed  some  refraction  disturbances,  not,  however,  of  a  serious 
character.  The  fog  chamber  was  connected  with  a  large  vacuum  chamber 
by  a  short,  wide  passageway,  though  width  is  of  little  consequence  here. 
The  cylinder  was  lined  with  wet  cloth,  closely  adhering,  except  at  the 
narrow  horizontal  windows  for  observation. 

For  exhaustion  the  stopcock  was  suddenly  opened  at  the  beginning 
of  the  first  second,  closed  after  5  seconds,  and  the  corona  quickly  measured. 
Filtered  air  was  then  at  once  introduced  and  the  next  exhaustion  made 
at  the  beginning  of  the  sixtieth  second.  This  rhythm  is  essential.  The 
isothermal  value  of  a  drop  of  pressure  [dp2]  was  carefully  predetermined. 
It  fixes  the  ratio  y  of  the  geometric  progression  of  nucleations,  since 


where  p  is  the  barometric  pressure  and  n  the  vapor  pressure  at  the  given 
temperature.  If  the  cock  were  left  open  for  a  longer  time  than  5  seconds 
[dpz]  would  increase  to  the  limit  dp3. 

The  goniometer  was  of  the  usual  type,  the  eye  being  at  the  center 
or  apex,  while  two  needles  on  radii  30  cm.  long  registered  the  angular 
diameter  of  the  coronal  disks  or  annuli.  Formerly  the  whole  instrument 
was  placed  on  the  near  side  of  a  fog  chamber,  the  eye  being  about  30  cm. 
from  the  nearest  wall.  It  conduces  to  much  greater  sharpness  of  vision, 
however,  and  admits  of  a  measurement  of  larger  coronas,  caet.  par.,  if 
the  eye  is  placed  all  but  in  contact  with  the  nearer  wall  and  the  needles 
(or  in  this  case  preferably  the  inner  edges  of  round  rods)  beyond  the 
further  wall.  In  such  a  case  the  refraction  errors  are  also  diminished. 
In  addition  to  these  advantages  I  may  mention  the  decidedly  increased 
(about  25  per  cent)  value  of  the  aperture  obtained.  These  excessive 
apertures  show,  however,  that  the  ordinary  diffraction  equation  for 
coronas  is  not  fully  applicable  ;  for  aperture  varies  with  the  position-  of 
the  eye  along  the  line  of  sight.  It  is  often  surprising  how  large  a  corona 
can  be  measured  by  the  second  method,  in  a  small  fog  chamber  scarcely 
6  inches  long.  The  distance  between  lamp  and  chamber  is  kept  about 
17=250  cm. 

23.  Equations.  —  The  equations  needed  in  the  present  work  are  derived 
in  my  last  report*  and  need  merely  be  summarized  here.  If  y  is  the 
exhaustion  ratio,  the  nucleation  nz  of  the  0th  exhaustion  in  terms  of  the 
original  nucleation  nQ  will  be 


where  5  is  a  subsidence  constant  and  5  the  chord  of  angular  diameter  of 
the  coronal  disk  on  a  radius  of  30  cm. 

*Carnegie  Institution  of  Washington  Publication  No.  96,  1908,  chapters  I,  in  (equat. 
i  to  12).  .  '.    .      "-  "  .    ,.  ,.    ... 


22    CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 

To  find  5,  two  consecutive  values  of  5  suffice,  or 


approximately.    The  diameter  of  particles  d  is,  in  terms  of  n 


If  ^  =  54.6X  io~6  cm.  is  the  wave-length  of  green  mercury  light  and  6 
the  angular  radius  of  the  first  green  minimum  of  the  coronas,  sin  0  =  o.6i 
A/(d'/2).  Since  sin  6  =  s/2R,  R  being  the  radius  of  the  goniometer  of 
which  5  is  the  chord,  d'  the  diameter  of  fog  particle  (the  primes  referring 
to  optic  measurements), 

d'  =  0.004/5 
for  mercury  light.    Hence  optically  the  nucleation  is 


where  m  grams  of  water  are  precipitated  per  cubic  centimeter  on  ex- 
haustion, and  found  in  the  exhausted  fog  chamber. 

24.  Data  with  white  light.  —  The  results  in  the  following  tables  are 
reported  in  accordance  with  the  same  plan  throughout.  The  fog  chamber 
is  initially  at  atmospheric  pressure  p,  the  vacuum  chamber  exhausted  to 
p  —  dpf.  When  the  exhaustion  cock  is  closed  5  seconds  after  exhaustion, 
the  pressure  in  the  fog  chamber,  after  the  original  temperature  is  rees- 
tablished, will  be  p  —  [dp2]-  The  common  isothermal  pressure  in  vacuum 
and  fog  chambers  when  communicating  after  the  exhaustion  is  eventually 
P  —  dp&  K  *  is  the  vapor  pressure  at  the  given  (isothermal)  temperature, 
the  exhaustion  ratio  is 


The  amount  of  water  precipitated  per  cubic  centimeter  is  m  at  the 
temperature  and  pressure  given. 

TABLE  9.  — Standardization  of  the  fog  chamber.     Welsbach  burner  and  phosphorus. 
Cock  open  5  sec.    Observation  interval  60  sec.    Bar.  75.9  cm.  at  22°.    Temp.  26°. 
cm.;    ^3=17.4  cm.;    dp'=i&.6   cm.;    y=(p  — 11  —  [#/>2])/(/>~7r)==o-775; 


p  =0.229; 


grams  at  20°;    4.22  grams  at  26 


°     7r  = 


cm.     Gonio- 


meter in  front.    Distances  of  eye  and  lamp  30  cm.  and  250  cm.,  on  opposite  sides 
of  fog  chamber.    Radius  of  s,  R  =  30  cm. 


z 

Corona. 

j 

Z 

Corona. 

s 

z 

Corona. 

s 

I 

Fog 

25 

9 

g 

14 

17 

Cor. 

6.8 

2 

Fog 

22 

10 

gy 

13-5 

18 

Cor. 

5-8 

3 

Fog 

18 

ii 

y 

12.5 

19 

Cor. 

5-1 

4 

r' 

17 

12 

o 

"•5 

20 

Cor. 

4.0 

5 

r 

16 

*I3 

r 

10.5 

21 

Cor. 

3-0 

6 

V 

15 

14 

P 

9-5 

22 

Cor. 

2.0 

7 

g' 

15 

g7 

7-5 

23 

Cor. 

I  .O 

8 

g 

H 

16 

g' 

7-0 

*Two  identical  series  beyond  this. 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 


To  facilitate  comparison  with  the  later  work,  where  mercury  light  is 
used,  a  series  of  coronas  in  geometric  sequence  is  given  in  table  9,  in  which 
the  Welsh ach  mantle  still  furnishes  the  light.  Here  5  denotes  the  chord 
of  the  angular  diameter  of  the  coronal  disk  on  a  radius  of  R  =  30  cm.,  when 


20       .IB 


FIG.  3.  —  Charts  for  white  light  (Welsbach  burner),  5/30,  of  the  reddish  edge  of 
the  disk  of  coronas,  in  terms  of  a  number,  z,  of  the  successive  identical  partial 
exhaustions  in  the  series. 


FIG.  4.  —  Charts  for  green  mercury  light,  showing  the  coronal  apertures, 
of  the  edges  of  trie  greenish  disks  of  coronas,  in  terms  of  the  series  number 
z  of  the  partial  exhaustions.  Series  I  for  2-minute  intervals  between 
exhaustions,  series  II  for  i  -minute  intervals. 


24        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

eye  and  lamp  are  at  distances  30  and  250  cm.  on  opposite  sides  of  the  fog 
chamber.  The  colors  of  the  edge  of  the  disk  are  denoted  by  r  red, 
v  violet,  g  green,  etc.  The  number  of  identical  exhaustions  made  is  equal 
to  z  =  23.  Beyond  2=13  the  series  was  obtained  twice  with  identical  data. 
No  attempt  at  computing  nucleations  from  these  data  need  be  made, 
as  they  are  practically  identical  with  the  earlier  series  given  in  the  pre- 
ceding report.  In  fact,  in  fig.  3  the  s  values  or  apertures  have  been  con- 
structed in  the  curve  a  in  terms  of  the  number  of  the  exhaustion  z  in  the 
geometric  series.  At  b  corresponding  data  (Carnegie  Institution  of  Wash- 
ington Publication  No.  96,  table  35,  series  i)  are  taken  from  the  report 
in  question  and  represented  in  the  same  manner. 

The  feature  of  these  results  which  I  wish  to  accentuate  is  this,  that 
after  the  tenth  exhaustion,  i.  e.t  for  small  and  moderately  large  coronas, 
the  5-data  lie  nearly  on  a  straight  line.  In  curve  a  this  is  the  case  almost 
throughout,  or  at  least  until  the  coronas  become  so  large  as  to  be  vague 
and  filmy,  while  the  ends  of  the  fog  chamber  interfere  with  the  measure- 
ments. The  slopes  of  these  lines  are: 

In  case  a,  ds/dz =  0.95 

In  case  fr,  ds/dz =0.95 

or  about  the  same  in  both  cases. 

25.  Data  with  green  mercury  light,  10^  =  54.6  cm. — Table  10  and  figs. 
4,  5,  contain  corresponding  results  obtained  with  a  mercury  arc  lamp  as 
the  source  of  light.     Different  annuli  are  measured  and  the  chords  5,  on 
a  radius  of  30  cm.  are  distinguished  by  accents  as  follows : 
s'  is  the  chord  of  the  green  disk, 

s"  is  the  chord  of  the  inner  edge  of  the  first  green  ring, 
s"'  is  the  chord  of  the  outer  edge  of  the  first  green  ring. 
The  edges  are  fairly  sharp.    Hence 


may  be  taken  as  the  chord  of  the  first  green  minimum.     Optically  the 
diameter  of  the  particle  is  then  df  =  0.004/5. 

The  water  precipitated  per  cubic  centimeter,  m,  differs  with  the  drop 
of  pressure  dp3/  p  and  the  temperature.  Putting  nf  as  the  optical 
value  of  the  number  of  nuclei  per  cubic  centimeter  in  the  successive 
seven  parts  of  the  tables  the  data  are  : 


I06W 

n' 

Table  10: 

Grams. 

Parts  I  and  II  

4.1 

122  S9 

Parts  III  and  IV  ... 

4.12 

123  s9 

Table  n: 

Parts  V  to  VIII  

4.02 

120  S* 

STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 


TABLE  10. — Standardization  of  fog  chamber.  Coronal  disks.  Mercury  lamp.  Phos- 
phorus nuclei.  Cock  open  5  sec.  Temperature  24°.  [dp'^\  =  17.0  cm. ;  <J/>3=  17.6  cm. ; 
dp'=i8.g  cm.;  y=(p  —  7t  —  [dp2])/(p  —  7:)  =0.770;  <5/>.,/|>=  0.231 ;  ^  =  2.2  cm.  m  = 
4.iXio-6g. 


Inter- 

Ob- 

Inter- 

Ob- 

No. 

Corona. 

polated 

served 

S 

No. 

Corona. 

polated 

served 

s 

s' 

s' 

s' 

s' 

Part  I.  —  Interval  between  observations 

Part  III.  —  Goniometer    beyond     fog 

2  min.    Barometer  76.17  cm.  at  26°. 

chamber,    eye   at   wall.      Barometer 

Eye  and  lamp  distances  30  cm.  and 

75.82  cm.   at   25°.   ^=0.769;    8pa/p 

250  cm.    Goniometer  in  front. 

=0.233;  w  =  4.i  Xio~6g. 

i 

2 

3 
4 
5 
6 

7 

Vague 
Vague 
g 

1 

13-0 

12.  0 
II  .O 
10.  0 
9.0 

8.0 

7  .0 

12  ? 

ii  ? 
10.8 

9-9 
9.0 
8.0 
7  .0 

ii.  5 
10.6 
9.8 

8-9 
8.1 
7.2 
6.4 

i 

2 

3 
4 
5 
6 

7 

g 
g 
g 
Vague 
Vague 
Vague 
Vague 

23.0 

21.8 

20.7 

19-5 
18.4 
17.2 
16.1 

23 

22 
21 
2O 
19 

16 

15 

25 
24 

22.6 
21.4 
20.1 
18.9 
17.7 

/ 
g 

K 

6.0 

/  *  ^ 

S-4 

V   .   tf 

5.  S 

8 

g 

14.9 

14 

16.5 

9 

IO 



5-0 
4.0 

O     T^ 

3-4 

2.2 

O     «J 

4-7 
3-8 

9 

10 

g 

13-8 

12.6 

13-5 
13-0 

15.2 
14.0 

ii 

g 

n-5 

H.7 

12.8 

12 

Vague 

10.3 

10.5 

ii.  6 

Part  II.  —  The  same.    Interval  between 

13 

Vague 

9-2 

9-4 

10.3 

observations  i  min.   More  rapid  filter. 

14 

g 

8.0 

8.4 

I  c 

Vague 

6.Q 

7  -  ^ 

7   o 

•  o 

16 

»  t*5i*>~ 

w  .  *y 

/    o 

6.3 

/         -7 

6.7 

i 

Vague  g 

I6.4 

I6.5 

14.2 

17 

4.6 

o 

5.2 

/ 

5-4 

2 

Vague  v 

15-6 

15? 

13-5 

18 

3-5 

4.0 

4-2 

3 

Vague  v 

I4.8 

14  ? 

12.8 

19 

2.3 

2.3 

3.0 

4 

Vague  v 

14.0 

14? 

12.  I 

6 

Vague  v 
Vague  v 

13-2 
12.4 

13-9 
12.5 

ii.  5 

10.8 

Part  IV.  —  The  same,  repeated. 

8 

r 

ii.  6 
10.8 

ii.  6 

II  .2 

IO.I 

9.5 

i 

g 

21.7 

24 

23.6 

9 

10 

ii 

12 
13 

g 

Dull 
g 

jr 

IO.O 

9-2 

8.4 
7-6 
6.8 
6.0 

10.8 
9-5 
8.9 
7-9 
7.0 

6.2 

8.8 
8.1 

7-5 
6.8 
6.1 
c  .  c 

2 

3 
4 

6 

7 

g 

Vague 
Vague 
Vague 
Vague 
g 

20.6 

19.5 

18.3 

17.2 

16.1 
14.9 

19 

1  6 
15 

22.4 

21  .  2 
2O.  O 

18.8 
17.6 
16.4 

15 

16 
18 

1. 

5.2 
4.4 
3-6 

2.8 

5-5 
4-7 
4.0 

2.8 

o  *  o 

4.8 
4.1 

3-5 

2.8 

8 
9 

IO 

ii 

g 
g 
Vague 
Vague 

13-8 
12.7 

n-5 
10.4 

14-5 
13-3 

12 
10 

15-2 
14.0 

12.8 

ii.  6 

19 

2.O 

2  .O 

2  .  I 

12 

g 

9.3 

9.0 

10.4 

y 

13 

g 

8.1 

8.0 

9.2 

14 

& 

7-0 

7.0 

8.0 

15 

g 

5-9 

6.0 

6.8 

16 

g 

4-8 

5-0 

5-6 

17 

3-6 

4.0 

4.4 

18 

2-5 

2-5 

3-2 

In  parts  I  to  IV  of  table  10  the  angular  diameter  s'  of  the  green  disks 
only  was  measured.  The  diameter  5  of  the  corresponding  first  minima 
may,  however,  be  obtained  by  using  the  method  of  reduction  found  in 
parts  V  and  VI,  where  5  =  0.44  +  0.85  s'. 

In  parts  V  and  VI  the  data  for  s'  and  s",  the  angular  diameter  of  the 
inner  edge  of  the  first  ring  are  both  observed,  while  in  parts  VII  and  VIII 
data  for  s'  and  s'",  the  outer  diameter  of  the  first  ring,  appear. 


26        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

Turning  specifically  to  parts  I  and  II,  in  which  the  goniometer  is  in 
front  of  the  fog  chamber,  it  will  be  noticed  that  in  series  I  a  two-minute 
interval  between  exhaustions  has  been  (exceptionally)  introduced.  The 
result  is  not  good;  for,  as  fig.  4  shows,  there  is  a  sudden  break  of  the  curve 
after  the  seventh  exhaustion,  probably  due  to  time  losses  in  the  extra 
minutes.  The  reason,  however,  is  by  no  means  obvious.  In  series  II, 
for  i -minute  intervals,  there  is  no  break  and  the  locus  passing  through 
the  points  for  green  disks  (the  others,  not  marked  g,  are  to  be  disregarded) 
is  persistently  straight  throughout.  The  curves  show  for  series  I,  ds/dz  = 
i. oo,  green  points  only,  and  for  series  II,  ds/dz  =  0.80,  suggesting  a  time 
loss  in  the  first  case.  Compared  with  table  9,  the  values  of  ds/dz  should 
be  in  the  ratio  of  red  and  green  minima,  or 

dsr/dz:  dsg/dz  =  o.<)$  :  0.80  correspond  to  ^7^  =  63.0/54.6 

The  last  ratio,  1.15,  is  somewhat  short  of  the  former,  1.19. 

In  series  III  and  IV  the  pins  of  the  goniometer  are  behind  the  fog 
chamber,  the  eye  being  at  the  front  wall.  In  series  III  the  relation 

5'  =  2. 30+1. 15(19-0) 
is  remarkably  well  sustained  throughout,  and  in  series  IV 

5'  =  2. 50+1. 13(18-0) 
gives  a  good  account  of  the  green  coronas,  if  the  dull  cases  are  ignored. 

The  most  interesting  results  are  given  in  parts  V  and  VI  of  table  1 1 
and  fig.  6,  and  the  computations  have  been  fully  carried  out.  In  these 
cases  the  chords  on  a  radius  of  30  cm.  of  the  edge  of  the  green  disk  5', 
and  the  inner  edge  of  the  first  green  ring  5",  were  successively  observed. 
Fig.  6  contains  both  pairs  of  curves  and  their  linear  character  is  again 
astonishing.  We  may  write 
PartV:  5'  =  2.o  + 1.10(19-0)  $"  =  3.4+ 1.21(19-2) 

5  =  0.59+1.065'=  —  0.56  +  0. 965" 
Part  VI:     $'  =  2.0+  1.13(18-2)  $"  =  3. 3+  1.30(18-2) 

5  =  0.50+1.075'=  -0.44  +  0.935" 

where  the  minimum  is  located  midway  between  5'  and  5",  both  of  which 
are  fairly  well  demarcated. 

From  both  series  the  mean  value 

$  =  0.55+1.06         s'  =  -0.50+0.93  5" 

may  be  derived  for  the  general  reductions  in  this  and  other  cases  where 
5'  is  observed. 

With  the  given  value  for  5,  the  optical  data  for  the  diameters  of  the 
particles,  d'  =  0.004/3,  and  for  the  nucleation,  n'  =  120  53  were  computed. 

The  subsidence  constant 

S-*.'(l-W/yV) 

was  obtained  from  the  observations  between  2=13  and  0  =  19  and  a  mean 
datum,  5=i2,  accepted  as  most  satisfactory.  It  is,  then,  possible  to 
compute  n0,  the  original  nucleation,  as 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 


from  each  of  the  groups  of  values  specified.    The  mean  results  are:   in 
part  V,  n0  =  4,540,000 ;  in  part  VI,  =  3,430,000. 

Knowing  n0,  the  series  of  datafornucleation  given  under  nX  io~3,  table 
ii  follow.  From  these  the  diameter  io4d=  iggn~1{3  of  fog  particles  and 
the  apertures  s  =  o.oo4/d  are  finally  computed.  In  other  words,  n  and  d 
are  the  data  obtained  in  view  of  the  occurrence  of  geometric  series  of 
nucleations  with  allowance  for  subsidence. 


$0,60 


to,  so 


10,40 


0,30 


FIGS.  5,  6,  7. — Charts  for  mercury  light,  including  measurements  of  the  aperture  of 
the  disks  s',  of  the  aperture  of  the  inner  edge  s",  and  of  the  aperture  of  the  outer 
edge  s"',  of  the  first  green  ring,  in  terms  of  the  number  z  of  the  partial  exhaustion. 
Vivid  greens  marked  g,  greenish  g';  dull  not  marked.  Apertures  s/$o  often  displaced 
vertically  for  clearness. 


28        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


TABLE  1 1 . — Standardization  of  fog  chamber.  Mercury  lamp.  Phosphorus  nuclei.  Cock 
open  5  sec. ;  60  sec.  between  observations.  Barometer  76.4  cm.  at  25°.  Temperature 
23°.  Distance  to  lamp  250  cm.  Goniometer  behind,  it  =  2.  i  cm.  5  =  1 2.  [dpz]  =-  1 7.0 
cm.;  ^3=17.6  cm.;  ^'  =  18.9  cm.;  ^=0.771;  dp3/p  =0.231;  w=*4.oXio-6g. 


Part  V.  —  Coronal  green  disks  and  inner  green  edge  of  first  rings. 

No.  z 

Obs. 
s' 

Interp. 

Obs. 
f 

Interp. 
s" 

s 

,0-X,' 

io~3Xw' 

.o-'X, 

i99n-3 

0.2  %/n 
com- 
puted 

from  n. 

i 

gi  23 

21.8 

25-2 

23-6 

1-7 

1580 

4540 

.20 

33 

2 

gl  21 

20.7 

.... 

24.0 

22.4 

i!s 

1350 

3420 

•32 

30 

3 

.... 

19.6 

g  25 

22.8 

21.3 

1.9 

1160 

2580 

•45 

28 

4 

.... 

18.5 

g22 

21.5 

20.  i 

2.0 

974 

1940 

.60 

25 

5 

.... 

17.4 

g20 

20.3 

18.9 

2.  I 

810 

1450 

•76 

22.8 

6 

.... 

16.3 

g7  I9 

19.1 

17.8 

2.25 

677 

1080 

•93 

20.8 

7 

g'  15 

15.2 

.... 

17.9 

16.6 

2-4 

549 

800 

2.14 

18.8 

8 

gH 

14.1 

.... 

16.7 

15-5 

2.6 

447 

589 

2-37 

16.9 

9 

13-0 

.... 

15-5 

14-3 

2.8 

350 

432 

2.62 

15.3 

10 

gy 

11.9 

g  J5-5 

14.3 

13.  i 

3.05 

270 

313 

2-93 

13-7 

ii 

10.8 

g  *3 

13.1 

12.0 

3-3 

208 

225 

3-27 

12.2 

12 

g' 

9-7 

g'12 

11.9 

10.8 

3-7 

151 

3-67 

10.9 

13 

g8.5 

8.6 

10.7 

9-7 

4.1 

no 

no 

4.  16 

9.6 

14 

y' 

7-5 

g9-5 

9.4 

8.5 

4-7 

73-7 

73-8 

4-74 

8.4 

15 

6.0 

6.4 

g' 

8.2 

7-3 

5-5 

46.7 

47-4 

5-50 

7-3 

16 

y' 

5-3 

g6.8 

7.0 

6.2 

6.4 

28.6 

28.3 

6.52 

6.1 

17 

gy4-s 

4.2 

5.8 

5-o 

8.0 

15-0 

14.9 

8.10 

5.0 

18 

y  3.0 

T.  .  i 

4.6 

T  .Q 

10.  3 

7    I 

10 

2.O 

o 

2  .O 

*T 

o  •  y 

2  .  7 

14.8 

/  •  •*• 
2    4. 

./ 

' 

/ 

1  •  *t 

Part  VI.—  The  same,  repeated. 

No.  z 

Obs. 
s' 

Obs. 
s" 

s 

t*X* 

IO-'X»' 

io-8Xtt 

,'££ 

computed. 

i 

g/27 

23-3 

1-7 

1520 

3430 

•32 

30.2 

2 

g22 

.... 

22.1 

i.S 

1300 

2580 

.46 

27.4 

3 

.... 

g  24 

20-9 

1.9 

1  100 

1940 

.60 

25.0 

4 

g22 

19.7 

2.0 

9l8 

1460 

.76 

22.7 

5 

g    20 

I8.5 

2.2 

760 

1090 

•94 

20.6 

6 

15.  E 

17-3 

2-3 

622 

811 

2.14 

18.7 

7 

g    14.5 

.... 

16.0 

2-5 

492 

600 

2-37 

16.9 

8 

13 

.... 

14.8 

2.7 

389 

441 

2.62 

15.2 

9 

gy  i 

g7    15-5 

13-6 

2.9 

301 

321 

2.92 

13.7 

10 

.... 

g  I3-5 

12.3 

3-3 

226 

232 

3-25 

12.3 

n 

g' 

g'12 

II  .2 

3-6 

168 

164 

3-66 

10.9 

12 

g8.2 

9-9 

4.0 

118 

"5 

4.12 

9-7 

13 

y 

g  10 

8.7 

4.6 

79 

77-7 

4.68 

8.5 

14 

8-5 

7-5 

5-4 

50 

50.4 

5-42 

7-4 

15 

.... 

7-2 

6-3 

6.4 

30 

30-5 

6.56 

6.3 

16 

y'4-9 

g' 

5-i 

7-9 

16 

16.5 

7.84 

17 

3-o 

3-8 

10.5 

6.8 

6-9 

10.5 

4.0 

18 

2.0 

2.7 

14.8 

2.4 

I.O 

STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 
TABLE  1 1 . — Standardization  of  fog  chamber — Continued. 


29 


Part  VII.  —  The  same.     Coronal  green  disks  and  outer  green  edge  of  first  ring. 

No.  z 

Obs. 
I* 

Interp. 
s' 

Obs. 

sm 

Interp. 
sm 

s 

d'  =  o.oo^/s 

io~3Xn' 

i 

18.6 

g33 

35-6 

20.3 

1.97 

1000 

2 

.... 

17-5 

g29 

33-5 

19.1 

2.09 

836 

3 

16.3 

?28 

3i-3 

17.9 

2.23 

688 

4 

g'i6 

15-2 

.... 

29.  2 

16.7 

2.40 

559 

5 

gi4 

14.1 

.... 

27.1 

15-5 

2.58 

446 

6 

g  13-5 

12.9 

.... 

24.9 

14-3 

2.80 

350 

7 

g7  ii.  i 

n.  8 

.... 

22.8 

i3-i 

3-05 

270 

8 

.... 

10.7 

g2I 

20.7 

11.9 

3.36 

202 

9 

g' 

9-5 

?I9 

I8.5 

10.7 

3-74 

147 

10 

g8.5 

8.4 

16.4 

9-5 

4.21 

103 

ii 

gg7-6 

7-3 

.... 

14-3 

8-3 

4.82 

68.6 

12 

g7 

6.2 

12.5 

12.2 

7-i 

5-63 

43-o 

13 

g5-5 

5-0 

IO.O 

5-9 

6.78 

24.6 

H 

g* 

3-9 

g8.o 

7-9 

4-7 

8.51 

12.5 

15 

2.8 

6.0 

5-8 

3-5 

11.4 

5-i 

16 

.... 

1.6 

4-5 

3-6 

2.3 

17.4 

i-5 

17 

.... 

•  5 

3-o 

i-5 

i.i 

36.4 

.2 

Part  VIII.  -The  same  repeated. 

j 

S22    ^ 

IQ    2 

•«  8 

21  .O 

I    QO 

1  1  IO 

2 

'  •  J 

A  V  •  •* 

18.1 

g35 

jo  •  u 
33-9 

19.8 

A    *  y-' 

2.02 

930 

3 

.... 

17.1 

g32 

32.0 

I8.7 

2.13 

785 

4 

16.0 

29 

30.0 

I7.6 

2.27 

654 

5 

g'lS 

14.9 

28.1 

I6.4 

2-43 

529 

6 

gi3-8 

13-8 

26.2 

15-3 

2.6l 

430 

7 

g  12.5 

12.8 

24.2 

I4.I 

2.84 

336 

8 

gy 

11.7 

g22 

22.3 

13-0 

3-08 

264 

9 

10.6 

g2I 

20.4 

ii.  9 

3-35 

202 

10 

9.6 

18.4 

10.7 

3-74 

147 

ii 

g' 

8-5 

g'ifi'-S 

16.5 

9-6 

4.17 

1  06 

12 

g7-5 

7-4 

14.6 

8.4 

4.76 

71.2 

13 

g7 

6.4 

g  12.  I 

12.7 

7-3 

5.48 

46.7 

H 

gy 

5-3 

g  10 

10.7 

6.2 

6-45 

28.6 

15 

4-2 

g8.7 

8.8 

5-o 

8.00 

15-0 

16 

.... 

3-i 

6.8 

6-9 

3-9 

10.3 

7-i 

i? 

.... 

2.  I 

5-0 

4-9 

2.7 

14.8 

2.4 

18 

.... 

I  .0 

3-5 

3-0 

1.6 

23-5 

•  5 

All  the  results  shown  in  table  1 1  have  been  constructed  graphically  in 
figs.  8  and  9  for  parts  V  and  VI  of  the  tables,  respectively.  The  observed 
and  computed  apertures  5  are  first  given;  then  the  observed  or  optically 
computed  d' ',  and  the  computed  d  from  sequences  appear,  and  finally  the 
observed  or  optic  n'  and  the  computed  nucleation  n  from  sequences. 
The  corresponding  data  coincide  very  closely  after  nine  or  eleven  ex- 
haustions, i.  e.,  for  moderately  small  and  small  coronas;  but  in  the  case 
of  large  coronas  and  nucleations  there  is  marked  systematic  divergence. 
A  discussion  of  these  results  will  be  given  presently. 


30         CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


0 


is      zo 


FIGS.  8,  9. — Nucleations  w,  n',  coronal  apertures  s/^o,  and  diameters  d,  d',  of  fog  parti- 
cles observed  and  computed  for  the  successive  partial  exhaustion,  number  z. 

Finally,  parts  VII  and  VIII  of  table  n  contain  measurements  of  the 
chord  of  the  angular  diameter  (radius  of  30  cm.)  of  the  outer  edge  of  the 
green  disk  sf  and  the  outer  edge  of  the  first  ring  5'".  The  minimum  may 
be  deduced  from  sf ',  since  5  =  0.54+  1.065'  has  been  accepted.  From  s  the 
optic  value  of  diameter  of  fog  particle  d'  and  the  nucleation  n'  has  been 
computed.  The  apertures  are  very  fully  given  in  fig.  7,  in  relation  to  the 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER.  31 

number  z  of  the  exhaustion.  The  curves  are  again  linear  in  character, 
but  in  case  of  the  outer  edge  5'",  the  insufficient  size  of  my  fog  chambers 
and  the  greater  vagueness  of  definition  interferes  with  close  measurement. 
The  results  are — 

Part  VIII:     s'  =  i.oo-f  1.07  (18-2)  $'"  =  3.004- 1.93  (18-2) 

5  =  1.614-1-14  (18—  z) 

Part  VII:     $'  =  0.50+1.13  (17-2)  s"f  =  1.50+  2.13  (17-2) 

5  =  1.08+  1.20  (17—0) 

As  a  rule  s'"  is  less  than  twice  s'.  The  data  for  5'  and  5  are  obtained 
alternately,  as  the  table  shows,  the  green  color  passing  from  the  disk  of 
the  first  ring  and  returning  again  in  succession. 

26.  Inferences.  Interference  and  diffraction. — The  tables  and  charts 
show,  in  the  first  place,  that  the  disk  and  first  ring  of  the  coronas 
are  alternately  vivid  green,  other  colors  being  dull  because  the  remaining 
lines  of  the  mercury  spectrum  are  faint.  At  intervals  neither  disk  nor 
ring  are  quite  green.  Hence  there  is  a  periodic  term  impressed  on  the 
diffractions,  which  may  be  identified  as  an  interference  similar  to  the 
case  of  the  lamellar  grating  referred  to  in  another  paper.* 

When  monochromatic  light  is  used  it  is  necessary,  therefore,  to  observe 
both  the  edge  of  the  disk  and  the  inner  edge  of  the  first  ring,  for  neither 
appear  vividly  at  the  same  time.  The  chord  5  on  a  radius  of  30  cm.,  for 
the  minimum  in  terms  of  the  corresponding  chords,  s'  and  5",  of  the  first 
and  second  edges  specified,  may  then  be  written 

5  =  0.55+1065'  5=— 0.50+935' 

Probably  the  ratio  5/5'  and  5/5"  should  be  constant  and  the  absolute 
term  in  these  equations  is  an  error  of  observation;  but  as  it  is  small 
little  depends  upon  it,  millimeters  only  being  significant. 

If  we  summarize  all  the  observations  for  ds/dt,  the  agreement  as  a 
whole  is  in  keeping  with  the  nature  of  the  observations  and  reasonably 
satisfactory.  Thus  in 

Series  I,  II,  ds'/dz=*o.go         5  =  0.44 +  0.855' (goniometer  in  front) 
HI,  1.15 


IV,  1.13 

V,  1. 10 

VI,  1.13 

VII,  1.13 

VIII,  1.07 


s  =  0.55  +  1.065'  (goniometer  behind) 
mean  ds'  /dz=i.i2 


*Amer.  Jour.  Sci.,  xxv,  p.  224,  1908. 


32        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

The  astonishing  feature  of  these  data  is  the  occurrence  of  linear  loci 
for  5  and  z  nearly  throughout  the  extent  of  the  curves.  It  is  as  difficult 
to  even  conjecture  a  reason  for  this  as  it  is  easy  to  find  reasons  against 
it.  The  presumptive  equation  for  5  is 

s  =  o.oo4(7T/6m)1/3w1/3      oc-i/n 
and  for  nz  if  TT  denotes  the  product 


Hence 


If  we  disregard  the  subsidence  correction    /  /  for  large  coronas 

ds/dz  oc//3 

in  which  there  is  no  suggestion  of  a  sustained  constancy  of  the  coefficient 
ds/dz  such  as  the  experiments  show. 

To  come  to  some  conclusion  as  to  the  cause  of  the  discrepancy  between 
the  optic  value  of  the  nucleation  nf  and  the  presumable  value  n  (geo- 
metric progression),  we  may,  as  in  table  12,  compare  the  successive  value 
n'z+i/n'z  —  sz+iS/sz3  m  their  relation  to  y  =  0.771,  the  exhaustion  applied. 
The  table  shows  that  for  very  large  coronas  n'z+lln'z>y,  whereas  for 
very  small  coronas  n'z+1/n'z<y.  For  the  intermediate  coronas  (gs), 
i.  e.,  from  the  seventh  to  the  tenth  exhaustion  among  twenty,  the  ratio 
is  nearly  equal  to  y.  Ratios  smaller  than  y  may  be  reasonably  inter- 
preted as  due  to  subsidence  and  the  subsidence  constant  5  is  actually  of 
the  order  of  values  to  be  computed  from  the  viscosity  of  the  medium 
and  the  size  of  the  vessels  and  fog  particles.  Within  this  range  (coronas 
smaller  than  g3)  the  optic  and  the  presumptive  nucleation  may  in  fact 
be  brought  into  agreement. 

In  case  of  the  large  coronas,  however,  subsidence  is  virtually  absent 
and  the  occurrence  of  n'z+l/n'z>y  calls  for  some  apparent  production  of 
nuclei  at  each  exhaustion,  which  is  naturally  altogether  improbable.  In 
table  12  I  have  therefore  additionally  inserted  n'  and  n  —  n',  the  latter 
showing  the  number  of  nuclei  not  registered  by  condensation. 

For,  no  matter  whether  condensation  on  a  given  group  of  nuclei  occurs 
or  not,  no  matter  how  many  nuclei  have  failed  of  catching  a  charge  of 
water,  the  removal  of  nuclei  by  partial  exhaustion  must  take  place  in  the 
same  way.  Such  removal  is  independent  of  condensation  and  would 
occur  in  a  dry  atmosphere  under  similar  treatment.  Consequently  y  can 
not  be  too  large.  It  may  be  too  small  not  only  from  subsidence,  but  from 
time  losses  (decay)  or  as  the  result  of  the  purification  of  air  due  to  turbu- 
lent motion  across  a  solid  or  liquid  surface.  Consequently  n  may  be 
regarded  as  an  inferior  limit  of  the  nucleation  with  a  probably  close 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 


33 


approximation  to  the  true  value.  A  comparison  of  n  and  n  —  n'  would  in 
such  a  case  show  the  percentage  of  nuclei  of  irregular  size  which  have 
failed  of  capture,  the  number  being  n  —  n' . 

At  the  same  time  it  must  always  be  recalled  that  no  adequate  theory 
of  coronas  exists  and  that  therefore  the  meaning  of  n'  is  obscure.  We 
must  in  any  case  place  a  part,  if  not  all,  the  discrepancy  between  n  and 
n1  within  the  province  of  such  a  theory.  The  need  of  it  is  particularly 
manifest  for  the  large  coronas,  in  which  there  is  accentuated  superposition 
of  interference  and  diffraction.  Small  coronas  may  be  tested  by  coinci- 
dent results  obtained  from  subsidence,  and  the  agreement  is  then  well 
within  the  errors  of  observation. 

12.  — Comparison  of  nucleations. 


Part  V. 

Part  VI. 

z 

**+,'/ 

sz*y 

Sn+Js, 

lo-V 

io~3(n-n') 

z 

W/ 
s,3y 

SM+I/S, 

io-V 

io-8O-o 

j 

0.90 

0.86 

1580 

2960 

i 

.  n 

0.86 

1520 

1910 

2 

.89 

.86 

1350 

2070 

2 

.10 

.84 

1300 

1280 

3 

.92 

.84 

1160 

1420 

3 

.09 

•84 

1000 

940 

4 

•93 

•83 

974 

966 

4 

.08 

•83 

918 

542 

5 

.92 

.84 

810 

640 

5 

.06 

.82 

760 

330 

6 

•95 

.81 

677 

403 

6 

•03 

•79 

622 

189 

7 

•95 

.81 

549 

251 

7 

•03 

•79 

492 

108 

8 

.98 

•79 

447 

142 

8 

.01 

•77 

389 

52 

9 

.00 

•77 

350 

82 

9 

•97 

•75 

301 

20 

10 

.00 

•77 

270 

43 

10 

.96 

•74 

226 

6 

ii 

.06 

•73 

208 

17 

n 

.91 

.70 

168 

-4 

12 

.06 

.72 

151 

8 

12 

.87 

•67 

118 

-3 

13 

.14 

.67 

no 

0 

13 

•83 

.64 

79 

—  i 

H 

.22 

•63 

74 

0 

14 

•77 

•59 

50 

0 

15 

.26 

.61 

47 

0 

15 

.68 

•53 

30 

0 

16 

.46 

•53 

29 

—  I 

16 

•56 

•43 

16 

0 

i? 

•63 

.48 

15 

0 

17 

•45 

•34 

7 

0 

18 

2.32 

.  33 

7 

18 

2 

—  I 

IQ 

OO 

/ 

-2     A 

In  the  first  eight  exhaustions  there  is  an 

In  both  cases  V  and  VI  there  is  accession 

apparent  production  of  nuclei. 

of  nuclei  at  first  and  withdrawal  finally. 

EFFICIENCY  OF  LARGE  AND  SMALL    FOG    CHAMBERS,  ATTACHED    TO 
THE  SAME  VACUUM  CHAMBER. 

27.  Fog  chambers. — The  large  apparatus  used  in  the  experiments* 
for  the  displacements  of  ions  showed  relatively  low  degree  of  conden- 
sational efficiency.  It  was  therefore  thought  worth  while  to  compare 
fog  chambers  both  larger  and  smaller  than  the  normal  size  (No.  i)  with 
regard  to  their  powers  in  catching  nuclei.  In  addition  to  the  large  re- 
ceiver (No.  2)  specified,  an  exceptionally  small  fog  chamber  (No.  3) 
was  specially  constructed.  Experiments  were  made  with  each  in  turn, 
both  for  the  case  of  the  vapor  nuclei  of  dust-free  air  and  of  ions. 

*See  chapter  III,  fig.  12. 


34        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

The  dimensions  of  the  three  fog  chambers  were: 


Number. 

Apparatus. 

Length. 

Diameter. 

i 

Old  cylindrical  

cm. 
4.5 

cm. 

12 

2 

3 

Large  conical  
Small  cylindrical  .... 

no 
16 

14  tO  22 
II 

The  axes  were  in  all  cases  horizontal  and  care  was  taken  to  insure  the 
occurrence  of  saturated  air. 

It  is  interesting  to  note  that  immediately  after  the  small  fog  chamber 
was  put  together,  there  was  an  internal  source  of  high  nucleation  active 
throughout  10  or  20  exhaustions,  a  result  frequently  obtained  in  other 
similar  cases.  It  is  none  the  less  difficult  to  detect  the  reason  for  its 
occurrence.  It  vanishes  completely  in  the  course  of  time.  It  is  probably 
identical  with  the  emanation  obtained  by  Russel*  from  metals  and  resins; 
at  all  events  its  eventual  evanescence  renders  it  harmless. 

28.  Data. — The  preliminary  data  are  given  in  table  13,  where  in  the 
case  of  small  apparatus  the  color  of  the  corona  was  chiefly  used  to  deter- 
mine the  nucleation.  The  ordinary  form  of  goniometer  would  have  been 
useless,  as  most  of  the  larger  coronas  transcend  the  limits  of  the  appar- 
atus. The  barometer  is  as  usual  denoted  by  p  and  the  sudden  drop  of 
pressure  after  the  return  of  isothermal  conditions  with  both  chambers  in 
communication,  by  dp]  n  is  the  estimated  nucleation  per  cubic  centi- 
meter. 

These  results  are  given  with  sufficient  detail  graphically  in  fig.  i ,  and 
are  compared  with  the  curves  holding  for  the  normal  apparatus,  No.  i, 
taken  from  a  preceding  report  for  identical  exhaustions.  In  case  of  the 
large  vessel,  No.  2,  it  was  impracticable  to  carry  the  exhaustions  very 
high  because  of  the  danger  of  breaking  the  vessel. 

The  results  show  that  fog  and  rain  limits  are  not  materially  changed, 
no  matter  whether  large  or  small  apparatus  is  used.  But  few  experi- 
ments were  made. 

The  efficiencies  of  the  apparatus,  however,  differ  in  marked  degree. 
In  case  of  the  large  apparatus,  No.  2,  less  than  150,000  vapor  nuclei 
respond,  even  at  the  highest  exhaustions.  The  number  of  nuclei  caught 
increases  pretty  uniformly  with  dp/p,  even  beyond  the  limits  tested, 
but  the  efficiency  is  enormously  lower  than  obtained  for  No.  i ,  where 
1,500,000  to  2,000,000  is  the  maximum  number  caught.  The  small 
apparatus,  No.  3,  is  even  in  excess  of  this  value,  inasmuch  as  over 
3,000,000  nuclei  per  cubic  centimeter  are  precipitated,  while  for  equal 

*Russel:    Proc.  Roy.  Soc.  London,  LXI,  424,  1897;  ivXin,  102,  1898. 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 


35 


values  of  dp/p,  it  is  nearly  twice  as  efficient  as  No.  i.  What  is  particu- 
larly interesting  is  the  definite  occurrence  of  coronas  of  the  first  order,  viz: 
the  crimson  clf  and  the  red  rlf  above  the  green  g2.  The  observer  is  left 
in  doubt  as  to  this,  unless  correlative  measurements  of  aperture  are  made, 
which  in  case  of  table  1  3  was  not  feasible  for  so  small  apparatus.  Such 
results  are  given,  however,  in  table  14. 

13.  —  Comparison  of  large  and  small  fog  chambers.    Dust-free  air.    Fog  chamber 
,  length  1  10  cm.,  diameter  14  to  22  cm.  ;  fog  chamber  No.  3,  length  16  cm.,  diam- 


No. 2 


eter  ii  cm. 


dp/p 

s 

io~3n 

dp/P 

$• 

io~8n 

Fog  chamber  No.  2*  Barometer 
76.35  at  25°. 

Fog  chamber  No.  3.    Barometer 
76.69  at  27°. 

0.202 

.248 
.287 
.296 
.340 
.360 

.405 
.440 

T 
2.6 

2.7 
4.0 
4.6 

6.2 

gbp7.o 

r 
4-5 
5-i 
19.2 
30.2 
80.6 

120.0 

0-334 

•348 
.360 
•370 
.385 
•396 
.364 

4 

g'    5-2 
g     7-2 

9-7 

g  10.2 

b  10.5 
c    9.0 

19 
40 

157 
440 
910 
1070 
310 

Fog  chamber  No.   3,  with  wet 
cloth  lining. 

Fog  chamber  No.  3.f  Barometer 
76.43  at  25°. 

0.335 
.362 
.385 
.410 

•433 
.600 

i-9 
7.0 

10.8 

12.0 

r 
r 

2 
144 
9IO 
22OO 
2900 
3470 

0.241 
.262 
.288 
•313 
•338 
.360 
.388 
.410 
.420 
.460 
.481 
.501 
.528 

o 
I 
I 

2 

4 
c 

g 

vp 
c 
r 
o-r 
o-r 
o-r 

O.  2 
.  2 

•3 

19 

106 
912 
1560 

2  2OO 
3000 
3000 
3130 
3220 

*Not  quite  free  from  leak, 
f  Freshly  put  together,  shows  an 
internal  source  of  nucleation 
throughout  10  or  20  succes- 
sive exhaustions. 

All  fog  chambers  which  have  aged  are  free  from  internal  sources  of 
nuclei,  whereas  when  freshly  installed  they  may  generate  them  through- 
out many  successive  exhaustions.  Even  after  this,  production  of  nuclei 
is  still  appreciable  if  long  intervals  of  time  elapse  between  the  exhaustions. 
An  endeavor  was  made  to  detect  the  nature  of  this  phenomenon,  but  a 
satisfactory  answer  has  not  yet  been  reached  beyond  the  surmise  given 
above.  The  production  is  observed  both  in  large  and  in  small  chambers 
and  the  nuclei  are  dust-like  in  size. 


36        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

34 


•36 


•38 


•3*        -34 
FIG.  10. — Condensational  efficiency  of  large  (i),  intermediate  (2),  and  small  (3)  fog 

chambers,  as  appearing  in  the  number  n  of  vapor  nuclei  of  dust-free  wet  air  caught  on 

exhausting  as  far  as  8p/p. 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 


37 


29.  Data  for  apertures. — To  identify  the  coronas  in  case  of  the  small 
vessel,  No.  3,  as  to  the  order  to  which  they  belong,  a  special  goniometer 
was  constructed.  In  using  this  the  eye  is  placed  at  the  nearer  wall  of  the 
fog  chamber,  while  the  two  round  vertical  rods  for  defining  the  angular 
aperture  are  placed  beyond  the  further  wall,  on  a  radius  of  30  cm.,  the 
eye  being  the  center.  The  inner  edges  of  the  rods  determine  the  aperture 
by  aid  of  a  sliding  scale  passing  across  them.  In  this  way  very  large 
coronas  may  be  measured  in  relatively  small  apparatus.  The  angular 


•50 


•54 


•58 


FIG.  xx. — The  same  as  fig.  10,  obtained  by  goniometer  measurement,  including  Wil- 
son's colors  and  the  effect  of  weak  radium. 


38        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


diameters  are  increased  (caet.  par.)  and  vision  is  at  an  advantage  as  to 
clearness.  Test  experiments  made  with  definite  coronas  showed  that  the 
aperture  s  of  the  old  goniometer  was  about  equal  to  0.9  5  of  the  new,  and 
with  this  number  the  reductions  needed  were  made  with  the  results  given 
in  table  14.  The  apparatus  showed  the  same  corona  for  the  same  dp/p 
on  a  number  of  successive  days,  so  that  fixed  conditions  had  been  reached. 

TABLE  14.  — Efficiency  of  the  small  fog  chamber,  No.  3,  with  special  goniometer. 
Length  16  cm.,  diameter  n  cm.,  2-inch  exhaustion  pipe.  Dust-free  air  and  ionized 
air.  Radium  I  ....  V,  axially  placed. 


Dust-free  air. 

Ionized  air. 

dp/p 

s 

io~*n 

dp/p 

.y 

io~3n 

I.     Barometer  76.54  at  25°. 

III.     Barometer   76.54  at   25°. 

0.249 

o 

o 

0.242 

0 

o 

.261 

.8 

.06 

.249 

.6 

.06 

•273 

I.O 

•23 

•251 

i.i 

.27 

.285 

i  .  i 

•30 

•255 

i-5 

•50 

.300 

1.4 

•50 

.268 

6.5 

48 

•314 

2.0 

i-5 

.282 

12.5 

360 

•327 

2-5 

3-3 

.288 

13-5 

436 

•340 

2.8 

4-5 

•  318 

14 

537 

II.     Barometer  76.85  at  23°. 

IV.     Barometer  76.85  at  23°. 

0.340 

3-o 

5-6 

0.277 

9-7 

159 

•350 

r    6.5 

57-4 

.308 

gy  14.0 

584 

.361 

c  10.8 

278 

•  378 

fro  13.0 

507 

.366 

*c  11.4 

335 

.472 

fr   12.0 

454 

•372 

ol  y  16.0 

599 

•540 

fc  11.5 

416 

.382 

bx  g  17-0 

1070 

•394 
.408 

•433 
•453 
.500 

•573 

v 

V 

r  18.5 

r 

O  21 
O 

1530 
1870 
2250 
2790 
3390 
4320 

V.       Radium    II     at     75     cm., 
observed   at  50  cm.  from  ex- 
haustion    end     in     large    fog 
chamber,    No.    2,    length   no 
cm.;    diameter   14  to   22   cm. 
Barometer  76.85  at  26°. 

0.194 

.217 

.... 

.... 

•  238 

i 

0.2 

.260 

3-5 

10.6 

.281 

gbp  7.2 

97.2 

•  326 

br7.8 

133 

.427 

7-7 

160 

VI.     Barometer  76.35  at  25°. 

.319 

p8-5 

169 

•367 

P8«5 

187 

•434 

p8.4 

208 

*Note  different  apertures'for  the  same  color. 
tCoronasjdecreasing  withlincreasing  precipitation. 


STANDARDIZATION    AND    EFFICIENCY    OF    THE    FOG    CHAMBER. 


39 


30.  Results. — The  results  are  constructed  in  fig.  1 1  in  comparison  with 
typical  results  for  apparatus  No.  i.     The  same  high  efficiency  already 
recognized  in  case  of  this  apparatus  in  table  13  is  again  exhibited,  the 
nucleation  caught  actually  reaching  over  4,000,000  per  cubic  centimeter 
or  invading  the  region  of  orange  coronas,  olf  of  the  first  order.    It  is  now 
probable  that  with  green  monochromatic  light  the  green  corona,  gt,  of 
the  first  order  may  actually  be  detected.    With  white  light,  however,  the 
initial  effect  is  a  mere  fog. 

A  number  of  trials  with  radium  (I  to  V,  within  the  chamber)  exhibited 
the  same  terminal  coronas  as  in  the  fog  chamber  No.  i .  Ions  are  caught 
with  the  same  facility  in  both  chambers  and  about  at  the  same  dp  I  p. 
In  other  words,  whereas  vapor  nuclei  are  caught  in  greater  number  by 
the  more  efficient  small  fog  chamber,  this  is  not  the  case  with  ions,  as 
comparisons  of  the  earlier  records  for  No.  i  show,  nor  with  the  positions 
of  the  fog  limit  and  rain  limit.  Moreover,  in  series  5  and  6,  obtained  with 
the  excessively  large  apparatus,  the  ions  are  appreciably  displaced  after 
condensation  has  begun,  showing  that  the  supersaturation  is  excessive. 

In  series  IV  there  is  a  pronounced  decrease  of  the  nucleation  with 
increasing  dp  I  p.  From  the  maximum  n  =  584,000  at  dp/p  =  o.$i,  the 
nucleation  drops  uniformly  to  n  —  416,000  at  dp/p  =  o.$4.  Inasmuch  as 
the  correction  for  increased  precipitation  has  been  applied  (smaller 
coronas  at  high  pressure-differences,  because  more  water  is  precipitated), 
this  result  is  to  be  associated  with  the  greater  removal  of  nuclei  at  high 
exhaustion.  The  coronas  show  the  number  of  nuclei  in  the  exhausted 
fog  chamber. 

The  smaller  nucleations  in  series  V  and  VI  are  referable  in  part  to 
the  weaker  radium  used  and  in  part  to  the  exceptionally  large  vessel 
employed. 

31.  Conclusion. — The  final  question  of  interest  is  a  revised  comparison 
of  these  results  with  C.  T.  R.  Wilson's  disk  colors,  if  his  two  extreme 
greens  are  interpreted  as  g2  and  gt  instead  of  g3  and  g2,  as  preferred  in  the 
preceding  report.*    In  such  a  case  the  nucleations  may  be  estimated  as 
follows: 


dp/p 

Color. 

nXio-3 

dXio« 

cm. 

0.360 

Fog  limit 

0 

.... 

•  384 

g 

800 

230 

.418 

g 

7,000 

1  20 

*Am.  Jour.  Sci.,  xxiv,  1907,  p.  309;  Carnegie  Institution  of  Washington  Publication 
No.  96,  1908,  sec.  35. 


40        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

As  far  as  w=  1,500,000  nuclei  per  cubic  centimeter,  this  curve  would 
still  lie  below  the  curve  for  the  small  apparatus.  It  then  crosses  and 
passes  beyond  it  to  a  limit  of  over  7,000,000  nuclei,  instead  of  4,000,000 
nuclei  per  cubic  centimeter,  estimated  for  the  small  fog  chamber,  No.  3. 
It  is  difficult,  of  course,  without  an  actual  measurement  of  aperture,  to 
come  to  a  conclusion  as  to  the  order  of  mere  colors,  but  the  possibility 
of  reaching  10,000,000  nuclei  per  cubic  centimeter  does  not  now  seem  out 
of  the  question.  The  probability  that  the  initial  white  fogs  seen  with 
ordinary  light  may  be  resolved  with  sufficient  clearness  for  measurement 
when  monochromatic  light  is  used,  has  already  been  suggested.  One  may 
notice,  however,  in  conclusion,  that  even  in  case  of  the  extreme  green,  the 
diameter  of  particle  would  still  be  over  twice  the  wave-length  of  light. 


CHAPTER    III. 

REGIONS  OF  MAXIMUM  IONIZATION,  AND  MISCELLANEOUS  EXPERIMENTS. 
REGIONS  OF  MAXIMUM  IONIZATION  DUE  TO  GAMMA  RADIATION. 

32.  Introductory. — I  have  recently*   standardized   the   fog  chamber 
by  the  aid  of  Thomson's  electron.    The  method  (as  will  be  shown  in  the 
following  chapters)  is  not  only  expeditious,  but  leads  by  inversion,  when 
my  old  values  of  the  nucleations  of  the  coronas  are  inserted,  to  values  of 
e  which  agree  with  Thomson's  and  other  estimates.     This  affords  an 
incidental  check  on  the  broader  bearings  of  the  work.    Before  describing 
these  experiments  it  will  be  expedient  to  refer  to  a  number  of  incidental 
results  bearing  on  the  work,  among  which  the  displacement  of  ioniza- 
tion  on  rapid  exhaustion  is  most  important.   This  has  been  studied  both 
in  long  and  in  short  fog  chambers. 

33.  Short  fog  chamber  (see  fig.   18,  below). — The  experiments  them- 
selves run  smoothly  and  take  but  a  few  minutes  each;   but  there  is  an 
inherent  difficulty  involved  in  the  interpretation  of  the  distributions  of 
ionization  observed  in  the  fog  chamber.    The  radium  (10  mg.,  ioo,oooX , 
contained  in  a  small,  thin,  sealed  glass  tube),  is  introduced  into  the  inside 
of  a  cylindrical  fog  chamber,  45  cm.  long,  by  aid  of  an  aluminum  tube 
(walls  i  mm.  thick  and  about  0.25  inch  in  diameter),  thrust  axially  from 
one  end  to  the  other  of  the  horizontal  chamber.     The  inner  end  of  the 
aluminum  tube  is  thoroughly  sealed ;  the  other  end  lies  quite  outside  the 
fog  chamber,  is  open,  and  serves  for  the  introduction  of  the  radium  tube. 
In  this  way  the  latter  may  be  moved  axially  from  the  glass  end  of  the 
fog  chamber  on  the  right  of  the  observer  to  the  metal  cap  which  closes 
the  fog  chamber  on  the  left. 

When  the  radium  is  placed  successively  at  distances  of  about  n  cm. 
apart,  within  the  available  45  cm.  of  the  length  of  the  fog  chamber, 
the  maximum  nucleation  (ionization)  coincides  with  the  position  of 
the  radium  when  both  are  near  the  glass  end  of  the  chamber  (i  2  cm.  in 
diameter).  The  nucleation  then  falls  off  rapidly  and  at  first  uniformly 
from  the  glass  end  to  the  metal  end,  where  the  coronas  are  strikingly 
smaller  and  the  nucleation  less  than  one-half  of  that  observed  at  the  glass 
end.  Considered  alone  this  would  appear  like  the  natural  effect  of  an 
increasing  distance  from  the  source,  except  that  the  coronas  near  the 
distant  end  approach  a  constant  diameter. 

*Am.  Jour.  Sci.,  xxvi,  pp.  87-90,  1908. 


42        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

When  the  radium  is  moved  about  1 2  cm.  (one-quarter  of  the  length  of 
the  fog  chamber)  from  the  glass  end  toward  the  metal  end,  the  maximum 
nucleation,  moving  at  a  greater  rate  toward  the  brass  end,  has  already 
outstripped  the  position  of  the  radium  and  now  lies  near  the  middle  of 
the  chamber.  The  coronas  and  the  corresponding  nucleations,  therefore, 
fall  off  rapidly  toward  both  ends.  In  other  words,  the  maximum  nucle- 
ation is  seen  where  there  is  no  radium. 

On  moving  the  radium  to  the  middle  of  the  chamber,  the  position 
of  the  maximum  nucleation  coincides  with  the  brass  end,  over  20  cm. 
beyond  the  radium.  The  coronas  now  fall  off  from  left  to  right,  to  a 
uniform  size  near  the  glass  end  of  the  chamber,  the  ratio  of  the  extreme 
nucleations  being  at  least  200,000  to  100,000  per  cubic  centimeter  in  the 
cases  examined.  Finally,  when  the  radium  is  placed  in  the  brass  cap  of 
the  chamber,  the  maximum  still  lies  there  and  the  nucleation  falls  off 
toward  the  glass  end,  but  all  nucleations  are  reduced  throughout  about 
one-half. 

It  is  clear  that  the  two  ends  of  the  chamber  behave  differently,  but 
no  simple  hypothesis  of  the  known  properties  of  the  rays,  at  least,  will 
account  for  the  occurrence  and  location  of  regions  of  maximum  nuclea- 
tion, nor  for  the  high  nucleation  ratios  specified.  Moreover,  plates  of 
lead  placed  outside  over  the  glass  end  of  the  chamber  to  modify  the 
secondary  radiation  are  quite  without  effect.  Covering  the  aluminum 
tube  with  a  thick  lead  pipe  the  phenomenon  is  slightly  reduced  in  magni- 
tude, but  not  in  character.  It  follows  that  the  gamma  rays  are  chiefly 
concerned. 

34.  Behavior  after  removal  of  radium. — A  final  element  of  interest 
is  the  behavior  of  the  axial  aluminum  tube  after  the  radium  (in  small 
sealed  glass  or  aluminum  tubes)  has  been  removed.  The  internally- 
sealed  aluminum  tube  is  distinctly  radioactive  for  several  hours,  even 
though  gamma  rays  alone  have  passed  through  it.  The  activity  vanishes 
gradually,  and  more  quickly  if  the  ions  are  continually  precipitated  by 
exhaustion.  The  behavior  of  this  residual  nucleation  is  very  peculiar; 
if  the  aluminum  tube  is  pushed  into  the  fog  chamber,  axially,  from  the 
glass  end  as  far  as  the  middle,  the  part  of  the  chamber  around  the  tube 
shows  strong  coronas  on  exhaustion,  while  the  other  half  (toward  the 
brass  cap)  is  blank.  Something,  consisting  of  very  slow-moving  particles, 
gradually  diffuses  radially  out  of  the  aluminum  tube.  Of  course  it  is 
difficult  to  deny  with  assurance  that  merest  traces  of  emanation  decaying 
within  the  aluminum  tube  may  not  possibly  account  for  the  activity; 
but  what  is  remarkable  in  any  case  is  the  existence  side  by  side  of  a  region 
with  nucleation  and  a  region  without  it,  in  the  absence  of  anything  like 
a  partition.  The  fog  chamber  itself  must  at  all  times  be  scrupulously  free 


REGIONS    OF    MAXIMUM    IONIZATION. 


43 


from  infection  such  as  an  emanation  would  produce,  and  anything  of 
this  kind  is  at  once  detected. 

35.  Long  fog  chamber. — After  obtaining  these  results,  the  work  was 
resumed  with  the  aid  of  a  larger  fog  chamber,  F  F,  fig.  12,  conical  in 
shape,  no  cm.  long,  22  cm.  in  diameter  at  the  broad  end,  tapering  down 
to  14  cm.  at  the  small  end,  E,  whence  the  exhaustion  took  place.  It  was 
so  mounted  as  to  place  the  axis  slightly  inclined  above  the  horizontal, 
in  order  that  an  even  depth  of  water,  w,  from  end  to  end,  might  be  stored. 
In  the  first  experiments  the  large  end  was  of  glass,  in  the  later  of  metal, 
but  this  difference  is  without  appreciable  effect  upon  the  present  results. 
In  each  case  a  hole  H,  2  or  3  cm.  in  diameter,  was  available  near  the 
center  of  the  large  end  for  the  introduction  of  an  axial  aluminum  tube 
AR  (walls  o.i i  cm.  thick),  running  from  end  to  end  of  the  chamber  and 
closed  at  R  within  it.  In  the  inside  of  this  tube  the  sealed  radium  tube- 
lets  could  be  moved  from  place  to  place,  in  a  way  similar  to  the  method 
followed  in  the  preceding  experiments.  No  wet-cloth  lining  was  intro- 
duced, because  the  experiments  had  to  be  performed  so  slowly  that 
saturation  in  case  of  a  clean  fog  chamber,  to  which  water  adheres  in  an 
even  film,  was  assured.  The  best  method  of  cleaning  is  vigorous  rubbing 
with  a  soft  rubber  probang,  as  for  instance,  a  thick  piece  of  rubber  tubing 
at  the  end  of  a  metal  rod.  Every  part  of  the  glass  must  be  scoured. 


FIG.  12. — Section  of  long  fog  chamber  with  hollow  aluminum  core. 

The  chamber  was  too  large  to  admit  of  the  capture  of  as  many  ions  for 
like  conditions  of  exhaustion  as  was  the  case  with  the  preceding  smaller 
apparatus,  but  this  difnciency  is  of  no  importance  here.  Filtered  air  is 
admitted  through  /. 

36.  Data. — Table  15  gives  an  example  of  typical  results  as  obtained 
both  with  the  glass  and  the  metal  capped  fog  chamber,  the  opposite 
(exhaustion)  end  being  always  of  brass.  In  the  first  two  parts  of  the 
table  the  chamber  was  not  quite  tight,  but  the  leak  was  sufficiently  insig- 
nificant to  virtually  filter  the  inflowing  air,  as  was  proved  by  the  direct 
experiments  and  by  the  third  part  of  the  table,  where  the  adjustment 
remained  quite  free  from  leak  throughout.  In  the  fourth  part  some 
miscellaneous  experiments  are  added.  Naturally  the  greatest  care  was 
taken  to  remove  water  nuclei. 


44    CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 


TABLE  15.  — Distribution  of  ionization.  Fog  chamber  no  cm.  long,  12  to  20  cm.  in 
diameter.  dp/p  =  25/76  =  0.33.  Distance  D  from  brass  or  exhaust  end  turned 
toward  glass  or  closed  end.  Radium  at  d. 


D  =  80  cm. 

D  =  50  cm. 

D  =  2o  cm. 

ft 

s 

io~*n 

s 

io~3n 

j- 

io~3n 

I. 

100 

gbp  8.0 

140 

7.2 

108 

6.3 

74 

80 

gbpy-9 

138 

7-9 

138 

7.0 

99 

50 

6.1 

66 

7.2 

108 

7-o 

99 

20 

4-9 

33 

5-4 

44 

5-i 

37 

35 

5-3 

4i 

5-6 

50 

6.1 

66 

65 

7-5 

119 

7-5 

119 

6.8 

90 

no 

7-5 

119 

6.6 

82 

5-i 

37 

II.     Both  ends  of  fog  chamber  of  metal  waxed. 

100 

8.0 

140 

7-i 

104 

5-2 

39 

80 

gbpy-8 

134 

P8.5 

174 

6.0 

62 

50 

5-8 

55 

7.2 

109 

gbp7-5 

119 

20 

4-7 

29 

4-9 

33 

5-4 

44 

80 

7-7 

130 

8.0 

140 

7.0 

94 

III.     The  same;  fog  chamber  quite  free  from  leak. 

80 

7-5 

119 

p  8.2 

161 

6-5 

87 

80 

gbp7-5 

119 

P8.4 

175 

6.2 

70 

50 

5-5 

47 

6.0 

62 

7-5 

119 

20 

5-9 

58 

5-6 

50 

5-9 

58 

IV.     Miscellaneous  experiments. 

*8o 

5-0 

35 

4-7 

29 

4.1 

20 

t8o 

8.0 

140 

9.0 

200 

7-8 

135 

tSo 

8.2 

155 

9.0 

200 

7-5 

119 

*  Core  charged  to  250  volts. 


t  Core  uncharged. 


t  Influx  at  large  end. 


The  results  are  also  shown  in  the  charts  figs.  13,  14  and  15,  the  two 
latter  being  the  more  typical.  The  abscissas  indicate  the  position  of  the 
axial  radium  tubelets  measured  in  centimeters  from  the  exhaustion  end 
of  the  fog  chamber,  the  ordinates  the  observed  nucleation.  The  three 
curves  correspond  to  three  goniometers,  placed  at  20,  50,  and  80  cm.  from 
the  exhaustion  end,  respectively.  The  results  are  seen  to  be  of  the  same 
nature  as  those  discussed  above. 

Fig.  14  shows  particularly  that  the  maximum  always  lies  on  the 
exhaust  side  of  the  position  of  the  radium.  Moreover,  the  ionization 
when  the  radium  is  near  the  exhaustion  end  is  always  small  and  nearly 
uniform  throughout.  The  maxima  are  largest  when  seen  in  the  middle 
(D=  50  cm.)  and  smallest  when  seen  at  the  exhaustion  end  (D  =  2o  cm.). 


REGIONS    OF    MAXIMUM    IONIZATION. 


45 


0 


10        £0         30       40        50        60       TO         80        90      iOOCTH. 


FIG.  13. — lonization  at  different  points  along  the  axis  of  the  fog  chamber  for 
different  positions  of  the  sealed  radium  tubelets  within  the  aluminum  core. 
Position  of  lines  of  sight  shown  on  the  curves. 


too  cm. 


FIG.  14. — lonization  at  different  points  along  the  axis  of  the  fog  chamber  for 
different  positions  of  the  sealed  radium  tubelets  within  the  aluminum  core. 
Position  of  lines  of  sight  shown  on  the  curves. 


46        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

In  the  third  part  of  the  table  the  occurrence  of  the  maximum  at  50  cm., 
for  radium  placed  at  80  cm.  from  the  exhaustion  end,  is  again  brought 
out.  Furthermore,  the  destructive  effects  of  electric  charge  on  the  insu- 
lated aluminum  core  extending  from  end  to  end  of  the  fog  chamber  are 
clearly  manifest,  the  number  of  ions  being  everywhere  relatively  very 
small.  Specially  favorable  conditions  obtaining  in  some  of  these  experi- 
ments are  accompanied  by  comparatively  large  ionizations  with  the 
uncharged  core.  This  part  of  the  table  also  contains  an  observation 
proving  that  if  filtered  air  enters  at  either  end  of  the  fog  chamber,  the 
result  is  the  same.  Identical  displacements  were  observed.  In  other 
words,  there  is  no  deficiency  of  saturation  involved  in  the  occurrence  in 
the  results  in  question,  nor  any  difference  between  the  freshly  filtered 
air  and  the  stagnant  residue  in  the  fog  chamber,  nor  any  effect  attribut- 
able to  parts  of  different  material. 

200 


9000. 


FIG.  15. — lonization  at  different  points  along  the  axis  of  the 
fog  chamber  for  different  positions  of  the  sealed  radium 
tubelets  within  the  aluminum  core.  Position  of  lines  of 
sight  shown  on  the  curves. 


REGIONS    OF    MAXIMUM    IONIZATION.  47 

37.  Inferences.  —  At  first  sight  one  would  conclude  that  in  a  region  of 
maximum  ionization  there  must  either  be  a  larger  rate  of  production  or 
a  smaller  coefficient  of  decay.  The  latter  might  be  expected  if  in  the 
given  region  the  ions  had  largely  the  same  sign.  The  frequent  occurrence 
of  the  ionization  ratio  2  to  i  in  the  earlier  work  lent  some  plausibility 
to  this  view,  but  the  later  experiments  with  a  much  longer  fog  chamber, 
and  where  much  greater  ratios  occur  in  the  ionizations  of  different  parts  of 
the  chamber,  quite  disprove  this  surmise.  The  correlative  view  that  the 
maximum  might  be  referred  to  the  superposition  of  primary  and  second- 
ary radiations  from  different  parts  of  the  fog  chamber  is  negatived  by 
changing  the  character  of  these  parts  from  glass  to  metal,  or  the  reverse. 
Hence  the  maximum  of  ionization  obtained  must  be  associated  with  the 
exhaustion  itself  for  in  each  case  the  displacement  of  the  maximum 
is  from  the  radium,  wherever  placed,  to  the  exhaustion  end  of  the  fog 
chamber.  And,  in  fact,  since  the  exhaustion  amounts  to  a  volume  ratio, 
vl/v,  if  vapor  pressures  be  neglected,  and 


where  p/  =  46  cm.  at  the  vacuum  chamber,  p  =  j6  cm.  at  the  fog  chamber, 
£2=51  cm.,  the  final  common  isothermal  pressure  when  both  chambers 
are  in  communication,  and  where  the  volume  ratio  of  the  chambers  [v/V] 
=  0.3  nearly,  the  exhaustion  is  about  v1/v=i.^^.  Hence  the  bodily 
displacement  of  air  at  the  exhaust  end  would  be  36  cm.,  and  at  the  middle 
1  8  cm.  if  the  fog  chamber  were  cylindrical.  The  conical  form  with  the 
small  end  at  the  exhaust  pipe  would  considerably  enhance  this  bodily 
transfer  of  air  from  the  closed  to  the  exhaustion  end  of  the  chamber. 
Thus  we  infer,  if  the  radium  is  at  the  closed  end,  that  is,  at  the  extreme 
distance  from  the  exhaustion  end,  the  maximum  should  lie  there  also, 
since  there  is  no  appreciable  displacement  of  air.  In  proportion  as  the 
radium  lies  nearer  the  exhaustion  end  of  the  fog  chamber,  the  displace- 
ment of  maxima  of  ionization  will  be  greater,  compatibly  with  the  greater 
bodily  displacement  of  air,  until  in  the  case  of  the  conical  chamber,  no 
cm.  long,  like  the  above,  the  displacement  may  exceed  40  cm.  Further- 
more, at  the  exhaustion  end  there  will  never  be  a  proportionately  large 
maximum,  because  the  ionization  has  been  removed  into  the  vacuum 
chamber,  and  the  whole  series  of  coronas  is  of  exceptionally  small  size 
throughout,  due  to  increasing  distance  from  the  radium.  In  fact,  it  can 
hardly  be  said  that  any  specific  evidence  of  the  occurrence  of  an  appre- 
ciable secondary  radiation  has  been  adduced  by  the  experiments. 

In  this  way  the  above  phenomena  are  at  least  qualitatively  accounted 
for,  as  it  must  be  acknowledged  the  displacement  is  often  larger  than  the 
data  here  estimated,  the  reason  for  which  is  not  sharply  determinable 


48        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

and  may  be  due  to  turbulent  motion  immediately  after  the  exhaustion. 
At  higher  exhaustions  the  distribution  is  often  more  uniform  and  other 
exceptional  conditions  supervene.  For  instance,  with  radium  at  d  =  So 
cm.  from  the  exhaustion  end  and  dp/p  =  o.4$,  nXio~3=i2o,  150,  140  at 
Z7  =  2o,  50,  80  cm.,  respectively;  with  a  tube  containing  six  radium  tube- 
lets  evenly  distributed  and  extending  from  ^  =  65  to  no  cm.,  the  corre- 
sponding data  at  dp/p  =  o.$3,  were  nXio~3=i55,  185,  240.  In  no  case 
was  more  than  a  single  maximum  encountered. 

Finally,  the  assumption  has  been  made  tacitly  that  the  ions  may  be 
removed  faster  during  the  exhaustion  and  displacement  than  they  can 
be  reproduced  by  the  presence  of  the  radium,  and  that  they  may  be 
caught  before  they  appreciably  decay.  To  take  the  example  of  the  above 
cases:  if  the  nucleation  is  equal  to  N  =  500,000  per  cubic  centimeter,  the 
production  would  bea  =  67V2=io~6X25Xio10=25Xio4or  250,000  nuclei 
per  second  per  cubic  centimeter,  nearly.  If  the  interval  of  displacement 
is  between  o.oi  second  and  o.i  second,  2,500  to  25,000  nuclei  should  be 
produced  to  replace  the  250,000  removed,  which  would  at  once  imply  a 
striking  difference  in  the  size  of  the  coronas  near  the  radium,  such  as  has 
actually  been  observed. 

In  conclusion,  therefore,  the  feature  of  great  interest  in  these  experi- 
ments is  the  definite  proof  contained  that  the  ions  may  be  displaced 
during  the  exhaustion  at  a  rate  much  faster  than  they  can  be  reproduced 
and  that  the  maximum  of  ionization  is  therefore  rarely  found  where  it 
was  generated. 

MISCELLANEOUS  EXPERIMENTS. 

38.  Experiments  to  detect  the  region  of  positive  ions.— In  table  16 
a  series  of  detailed  experiments  is  recorded  to  determine  the  character  of 
the  relation  between  the  drop  of  pressure  and  the  number  of  ions  captured 
in  the  fog  chamber  of  the  usual  shape  (No.  i,  section  27).  It  was  partic- 
ularly desirable  to  locate  the  rather  sudden  flexure  of  the  curve  of  dis- 
tribution between  its  oblique  and  its  horizontal  branches  and  to  see  if 
any  evidence  could  be  found  of  a  second  region  of  flexure  corresponding 
to  the  positive  ions,  by  aid  of  a  fog  chamber  like  the  one  in  question. 
The  method  of  two  independent  sources  was  employed,  the  coronas  being 
put  in  contact,  S  denoting  the  chord  on  radius  of  R  =  250  cm.,  or  if  2  Q 
is  the  angular  diameter  of  the  coronas,  5=2  R  tan  6.  It  was  not  thought 
necessary  to  reduce  5  to  the  number  of  nuclei  per  cubic  centimeter,  as  the 
former  is  in  some  respects  a  more  convenient  datum.  There  are  two 
independent  series  (see  fig.  16),  in  the  first  of  which  the  sealed  radium 
tubelet  is  on  the  outside  of  the  chamber,  in  the  other  on  the  inside  in  the 
axial  aluminum  tube.  In  both  cases  the  flexure  of  the  curve  lies  at  about 
dp Ip  =  0.285,  notwithstanding  the  decidedly  greater  nucleation  in  series  2. 


MISCELLANEOUS    EXPERIMENTS. 


49 


The  region  of  positive  ions  should  begin  at  about  dp/ p  =  0.31  cm.,  but 
neither  curve  shows  the  slightest  suggestion  of  any  increase  in  nucleation, 
though  the  drop  in  pressure  has  been  intensified  to  an  extreme  case.  Fog 
chambers  of  the  above  type  thus  refuse  to  admit  the  separate  occurrence 
of  positive  ions.  To  this  extent,  therefore,  the  statement  that  negative 
ions  only  are  captured  would  be  justified. 

m 


•25       *6       <&       -E8        -29       -30       -51         -3£      -38       -M       -35 
FIG.  1 6. — Absence  of  evidence  for  the  region  of  positive  ions  beyond  dp/p=o.^i, 
in  case  of  a  plug-cock  fog  chamber.    Aperture  5  in  terms  of  the  exhaustion  ratio 
dp/p. 

TABLE  16. — Endeavor  to  find  the  region  of  positive  ions  in  radium  curve. 


dp 

dp/P 

S 

Corona. 

dp 

dp/P 

5 

Corona. 

I.     Barometer    75.9    cm.;    temperature 
26.0°.  Radium  I  to  V  on  top.  D  =  7  cm. 

II.     Radium  I,  inside  of  fog  chamber. 
D=o.     Barometer  76.3  cm.;   temper- 
ature 24°. 

26.6 

0-350 

78 

gy 

19-5 

0.254 

10 

24.8 

•327 

80 

gy 

20.6 

.268 

67 

o 

23-5 

.310 

82 

gy 

21.0 

.274 

82 

g 

23.0 

.302 

79 

gy 

22.3 

.292 

102 

0 

21.9 

.287 

79 

gy 

22.8 

.298 

105 

o 

21-5 

.282 

76 

o 

24.8 

.324 

no 

o 

20.4 

.267 

5i 

0 

19.2 

.252 

13 

.... 

20.6 

.270 

50 

o 

21  .2 

.278 

68 

r 

21-5 

.282 

69 

r 

22.3 

.292 

78 

gy 

21.7 

.285 

76 

o 

50        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


39.  Radium  within  the  fog  chamber.  Sealed  tubes. — An  early  series 
of  experiments  on  the  observed  distribution  of  ionization  within  the 
chamber  due  to  the  presence  of  radium  in  different  parts  is  given  under 
special  treatment  in  table  1 7 .  Coronas  from  two  sources  of  light  were  put 
in  contact,  giving  S.  The  radium  was  placed  alternatively  1 2  cm.  from 
the  two  ends  of  the  fog  chamber,  45  cm.  apart.  The  lines  of  sight,  I  near 
the  brass  and  II  near  the  glass  end,  were  20  cm.  apart  in  the  middle  of 
the  available  length. 

TABLE  17.  — Radium  within  chamber.     Tubes  I-V.     Barometer  75.9;    temperature 
25.7°;  airS=i.o;   dp3=2$.o.    dp/p  =0.303. 


5 

Corona. 

nXio-3 

a  X  io~3  = 
bn?  (i  +  b/cn) 

I. 

Radium* 

near  brass-cap  end.    Observation  lines  20  cm.  apart. 

Observed  nea 

Observed  at  < 
Observed  at  j 

r  middle 

r     84 
82 

1       83 
92 

7i 

wp 
wp 
w  p 
w  r  o 
g 

268 
243 
258 
334 
159 

79 
68 
76 
124 
3i 

"ap  end    . 

jlass  end  . 

II.     Radium  near  glass  end. 

Observed  nea 
Observed  at  ( 
Observed  at  j 

r  middle 

1  06 
no 
9i 

wy 
wy 
wr 

5i7 
580 

334 

286 
356 
124 

>ap  end 

rlass  end 

III.     Fog  limits. 

ty,-  18.4 
4fc*i7.7 

0.9 
.0 

i  .0 
.0 

dP/P  =  0.2424          dpQ/P  =  0.240 
.2332                            .231 

Vj/v—i.215 
1.205 

*  Fog  chamber  cleaned  with  3  exhaustions. 

There  was  no  vertical  distribution  of  the  ionizations,  but  the  horizontal 
distribution  was  as  usual  very  evident.  Assuming  that  the  number  of 
ions  produced  per  second,  a,  is  given  by  a  =  bn2-\-cn  where  b  =  io~6  is  the 
decay  constant  and  c  =  0.036  an  absorption  constant.  The  values  of  a 
are  thus  as  follows: 


IO~3W 

io-3a 

Radium  at  I  (within  fog  chamber)  : 
Observed  at  I  

7-14 

124 

Observed  at  II 

I  5Q 

•7J 

Radium  at  II  (within)  : 
Observed  at  I 

•7  'I  A 

124 

Observed  at  II                                    .    . 

ceo 

^2O 

Radium  on  top  (outside)         

175 

-J7 

MISCELLANEOUS    EXPERIMENTS. 


A  few  rain  limits  were  incidentally  tested,  as  the  opportunities  were 
exceptionally  good.  These  data  are  given  in  part  III  of  the  table.  They 
have  the  usual  values  in  my  work,  dp/p  =  o.2$  orv1/v=i.2i,  and  lie  below 
Wilson's  values. 


40.  Distance  effect.  —  A  few  experiments  were  incidentally  made  to 
determine  the  effects  of  the  distance  D  of  the  radium  from  the  fog  chamber 
in  terms  of  the  numbers  of  ions  produced  per  second,  a,  where  a  =  bn2+cn, 
as  above  explained.  The  method  of  two  sources  (chord  S)  with  the 
coronas  in  contact  was  used.  Table  18  shows  the  chief  results. 


TABLE  18.  —  Distance  effect.    Radium  I  to  V. 
D  from  axis  of  fog  chamber.     Air,  .9=1.0. 
c=o.0356. 


Barometer  76.4;   temperature  21.6°. 
dps=22.8;    8p/ps=  0.298;    6  =  io~°; 


D 

5 

io~3Xn 

io~8X 
n2D*(i  +  c/bn) 

D 

S 

io~3Xn 

io-»X 

w2L>2(i  +  c/6w) 

*7.o 

4 

174 

1784 

IOO 

30 

13 

4630 

73 

167 

1656 

30 

13 

4630 

73 

167 

1656 

200 

22 

4.6 

7200 

20 

59 

92 

4720 

22 

4.6 

7200 

61 

104 

5800 

7 

72 

165 

1612 

50 

45 

4i 

7800 

44 

38 

6975 

*Radium  tube  lies  on  the  glass  vessel,  7  cm.  from  the  axis. 

Inferring  that  n2D2(i  +  c/bn)  should  be  constant,  the  following  com- 
parison results: 

D  —        7         20  50         TOO        200  cm. 

io-1Jn2£>3(i  +  c/6w)  -      1.7         5.2          7.4          4.6          7.2 

At  D  =  7  cm.  the  radium  is  too  close  for  any  law.  The  agreement  there- 
after is  an  attempt  at  constancy  in  so  far  as  the  small  coronas  beyond 
D  <  TOO  cm.  admit. 


41.  Attempt  to  calibrate  the  fog  chamber  with  5  separate  sealed  tubelets 
(I,  II,  III,  IV,  V)  of  radium. — These  results  are  given  in  table  19.  The 
tubes  were  placed  in  a  gutter  on  the  outside  of  the  chamber  at  a  dis- 
tance D,  or  in  a  sealed  aluminum  tube  within  the  chamber.  The 
table  gives  the  aperture  5  (two  sources  of  light),  the  nucleation  n  com- 
puted therefrom  and  the  number  of  ions  a  generated  per  second,  where 
a  =  bn2+cn  as  in  the  preceding  instance. 


52        CONDENSATION    OF    VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 
TABLE  19. -Calibration  with  radium  I  to  V. 


Radium. 

5 

Corona. 

nXio-3 

io~3a 

Computed 

aXio-3 

Part  I.     Barometer  75.9;  temperature  25.7°;  air,  S  =  i.o;  ^  =  23.0;  dp/p  =  o.^o^. 
Radium  I  on  top,  each  in  its  niche.     D=i  cm. 

200000X0  oio  g          ..II 

6s 

122 

IQ    2 

20  000  X                      V 

56 

78 

8  8 

10  oooX      I 

61 

IO2 

14.   O 

(Mean)        I  +  II  +  V 

74. 

w  r 

176 

•77    2 

4.2    O 

10  ooo  X    Ill 

c? 

71 

7    5 

looooX     IV 

cc 

74. 

8  i 

I  +   .     .   .  +V 

74 

g 

I76 

37-2 

57-6 

Part  II.     Repeated.    D  =  j  cm.     Barometer  75.3;    temperature  26.4°;    dp  =  23.0; 

dp/p  =  0.306. 

II  +  V  +  I 

68 

gg 

149 

27.5 

72 

g 

I69 

34-6 

.... 

72 

gy 

169 

34-6 

.... 

Part  III.     Larger  distance.    D=*  2  2  cm.  from  axis.    #/>/£  =0.306. 

II 

49 

55 

5-oo 

V 

.... 

32 

2.16 

.... 

I 

47 

.... 

50 

4.27 

.... 

III 

37 

.... 

25 

1.52 

.... 

IV 

35 

.... 

21 

1.19 

.... 

1+     .     .     .  +V 

60 

.... 

103 

14.2 

14.1 

1+    .     .     .  +V 

60 

103 

14-3 

Part  IV.     Higher  dp.     D  —  j  cm.     Air,  5=4.6.     Barometer  75.9;  temperature 

26.6°;   dpa—  26.6;  dp/p  =  0.350. 

II 

61 

"3 

16.8 

V 

56 

87 

10.7 

I 

63 

125 

20.0 

.... 

III 

54 

78 

8.9 

.... 

IV 

54 

78 

8.9 

.... 

I    ...  V 

79 

gy 

238 

65.1 

65-3 

Part  V.     Barometer  76.3;  temperature  24°;   dp3=>23.o;   dp/p*=o.$oi. 

II 

H5 

o 

400 

174 

V 

99 

ro 

260 

77 

.... 

I 

105 

0 

300 

100 

.... 

III 

93 

r 

210 

52 

.... 

IV 

95 

r 

225 

59 

.... 

I    ...  V 

130 

y 

570 

344 

461 

MISCELLANEOUS    EXPERIMENTS.  53 

The  results  in  parts  I  and  II  are  not  satisfactory.  Thus  the  separate 
determination  of  a  for  each  tube  added  together  are  much  larger  than  the 
corresponding  datum  for  the  tubes  abreast: 

I,  II,  V: 

Separately  .........................  a  =  42,000  ions  per  second. 

Together  ...........................       37,ooo 

I,  II,  III,  IV,  V: 

Separately  .........................       57,600 

Together  ...........................       37,ooo 

With  the  tubes  together,  a  certain  number  of  ions  apparently  failed  of 
capture,  but  this  is  not  the  case,  as  is  shown  in  table  16,  where  all  ions  are 
caught  for  dp/p  =  o.2%,  much  below  the  present  datum. 

The  third  part  of  the  table,  however,  shows  accordant  results,  giving 
14,000  ions  per  second  separately  and  14,300  when  the  tubes  are  acting 
together,  but  the  ionization  is  lower  (D  =  22  cm.). 

In  part  IV  the  drop  in  pressure  is  larger.  The  agreement  is  satis- 
factory, a  =65,  ooo  ions  per  second  when  the  tubes  act  together  and 
a  =  65,  ooo  when  their  separate  effects  are  added,  but  in  other  similar 
cases  the  results  were  not  so  good.  Thus  in  the  last  series  V,  the  separate 
and  joint  effects  are  460,000  and  340,000;  here,  however,  the  high  nucle- 
ation  is  due  to  the  presence  of  radium  within  the  chamber  in  sealed 
aluminum  tubelets,  and  the  diffuse  coronas  are  hard  to  measure. 

The  method  of  graduation  depending  on  the  use  of  sealed  batches  of 
radium,  together  and  separately,  has  not,  therefore,  given  trustworthy 
results.  The  chief  reason  for  this  is  that  the  rate  of  production  a  is  as  the 
sixth  power  of  the  aperture  5 


If  the  tubelets  were  equally  strong  their  sum  would  be 
which  is  about  the  relation  of  aperture  for  contiguous  crimson  and  green- 
yellow  coronas.  Hence  small  subjective  differences  play  a  large  part  in 
such  experiments. 


CHAPTER   IV. 


THE    STANDARDIZATION    OF   THE   FOG    CHAMBER    BY    THE    AID    OF 
THOMSON'S  ELECTRON. 

THE  CONSTANT  e,  EXPRESSED  IN  TERMS  OF  VELOCITIES  OF  THE  IONS. 

42.  Advantages. — Of  all  the  methods  which  I  have  tried  to  evaluate 
the  coronas  in  terms  of  the  number  of  nuclei  which  they  represent  under 
given  conditions  of  exhaustion,  the  above  method  is  the  most  expeditious 
and  promising.  A  single  experiment  need  take  but  a  few  minutes.  Inci- 
dentally the  observer  learns  whether  negative  and  positive  ions  have 
been  captured,  for  on  using  the  table  of  coronas  which  I  developed  here- 
tofore, the  value  of  e  may  be  computed  and  the  result  must  coincide  with 
Thomson's  datum. 

a 


JBC 


k 


j 


FIG.   17. — Fog  chamber  with  plate  electrical  condenser. 

43.  Plate. — These  experiments  were  of  a  tentative  character  and  the 
condenser  used  was  a  plate  of  brass  P,  of  area  .4  =  5X15  sq.  cm.  sus- 
pended at  a  distance  of  i  cm.  above  the  water  W,  and  parallel  to  it.  It 
was  supposed  under  these  circumstances  the  discharge  current  in  the 
presence  of  radium  in  sealed  aluminum  tubes  placed  at  R  in  fig.  17 
would  be  largely  confined  to  the  narrow  space  between  plate  P  and 
water  W,  which  was  earthed,  but  this  proved  not  at  all  to  be  the  case, 
as  will  be  seen  presently.  In  the  absence  of  radium,  the  leakage  was 
throughout  negligible,  the  conductor  a  being  sheathed  by  the  hard  rubber 
tube  6,  kept  dry  except  during  use.  The  fall  of  potential  was  measured 
by  a  graduated  galvanoscope,  whose  capacity  was  in  parallel  with  P. 
The  number  of  ions  n  was  found  from  the  aperture  of  the  coronas  on 
condensation.  We  may  therefore  write  for  the  charge  per  ion,  if  i  is  the 
distance  of  P  above  the  water-surface  W,  and  V  the  potential  difference 
in  volts 

Cl        V 


300  A  Un  V 


54 


STANDARDIZATION    OF    FOG    CHAMBER. 


55 


where  C  is  the  total  capacity  and  U  the  appropriate  velocity  of  the  ions 
in  the  field  of  i  volt  per  centimeter,  each  ion  carrying  the  charge  e,  in 
electrostatic  units,  positive  or  negative,  depending  on  the  charge  on 
the  plate. 

While  the  apparatus  as  a  whole  apparently  functioned  very  well,  it 
was  found  that  the  removal  of  the  plate  made  no  difference  whatever. 
Thus  if  D  is  the  distance  of  the  radium  from  the  fog  chamber: 


Condenser  plate  P  in  place. 

Condenser  plate  P  removed. 

D 

Leak. 

v/v 

D 

Leak. 

V/V 

cm. 

Volt/cm. 

cm. 

Volt/cm. 

40 

O.OOOI2 

0.00286 

40 

0.00028 

0.00242 

.... 

287 

30 

277 

.... 

289 

29 

260* 

15 

.00040 

475 

15 

635 

21 

547 

808 

M 

544 

720 

435 

o 

-OTOISf 

0 

.00021 

635 

.00975 

.... 

703 

995 

.... 

685 

*With  two  lead  plates  each  i  mm.  thick  covering  the  radium,  V/V=  .00298. 

fWith  two  lead  plates  each  i  mm.  thick  covering  the  radium,  V/V=»  .00800. 

The  results  (due  to  incidental  reasons)  are  thus  even  larger  in  the  absence 
of  the  plate  P  than  when  it  is  present,  although  the  conduction-leaks 
are  throughout  negligible.  It  is  therefore  impossible  to  interpret  the 
results  obtained  or  to  compute  the  e  from  them.  When  D  was  15  cm., 
or  larger,  the  effect  of  one  or  more  thin  lead  plates  over  the  radium  was 
no  apparent  deduction.  In  the  adjustment  given,  therefore,  the  whole 
region  of  the  radium  conducts  and  the  fog  chamber  is  merely  effective 
as  a  part  of  the  region. 

44.  Cylinder. — If  the  sealed  radium  tubelets  rr  are  inserted  by  aid  of 
a  wider  aluminum  tube  AR  (closed  at  one  end)  into  the  axis  of  the  cylin- 
drical fog  chamber  FF,  the  closed  end  A  projecting  within  as  in  fig.  18, 
the  difficulties  referred  to  are  in  a  measure  obviated.  Nevertheless,  in 
the  present  experiment  it  was  thought  preferable  to  use  the  fog  chamber 
for  measuring  the  number  of  ions  only,  while  an  independent  condenser 
was  installed  for  electrical  measurements. 

The  cylindrical  electrical  condenser  is  employed  as  follows:  A  closed 
aluminum  tube  0.62  cm.  in  diameter,  18  cm.  long,  containing  weak 
radium  in  sealed  tubelets  equally  distributed  along  its  inside,  is  made 
the  core  of  the  condenser,  the  outer  surface  being  2.1  cm.  in  diameter 
and  leaded  to  an  inch  or  more  in  thickness  beyond.  The  aluminum  core 
in  question  is  suspended  axially  from  a  fine  wire  leading  to  a  sensitive 


56        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

electrometer.  The  voltages  here  to  be  measured  must  of  course  be  small, 
and  hence  all  connecting  wires  are  to  be  inclosed  in  earthed  metal  pipes. 
The  core  in  question  is  then  removed  from  the  electrical  condenser  and 
put  into  the  axis  of  a  dust-free  fog  chamber  (fig.  1 8),  where  the  nucleation 
(ionization)  is  found  on  condensation  from  the  constants  of  the  coronas, 
or  vice  versa.  Here  there  are  some  outstanding  difficulties,  for  the 
coronas  are  not  the  same  throughout  the  length  of  the  fog  chamber,  as 
discussed  in  Chapter  III.  Even  immediately  around  the  radium  core  a 
single  corona  may  be  green  on  one  side  and  red  on  the  other.  In  a  fog 
chamber  45  cm.  long,  the  coronas  may  vary  from  the  glass  end  to  the 
metal  end  of  the  chamber  in  a  way  to  correspond  to  from  100,000  to 
200,000  nuclei,  respectively,  while  the  radium  core  is  fixed  in  the  middle. 
Inferring  secondary  radiation,  one  might  naturally  expect  to  obtain  still 
larger  coronas  near  the  metal  end  if  the  radium  core,  thoroughly  sealed, 
is  placed  there  instead  of  in  the  middle  of  the  chamber.  But  this  is  not 
the  case,  the  coronas  being  markedly  smaller  than  before,  decreasing 
uniformly  in  size  toward  the  glass  end.  As  the  sealed  aluminum  tube 
is  within  the  chamber,  this  behavior  is  clearly  of  great  importance. 


FIG.   1 8. — Fog  chamber  used  as  a  cylindrical  electrical  condenser.    AR,  aluminum  core. 

These  difficulties  are  inherent  in  the  phenomenon  and  merely  exhibited 
by  the  fog  chamber.  The  latter  has  the  great  advantage  that  enormous 
nucleations,  like  millions  per  cubic  centimeter,  are  not  excluded.  Under 
these  circumstances  the  coronas  alone  are  available  for  finding  the 
nucleation,  inasmuch  as  all  the  fog  particles  evaporate  before  subsidence. 
Finally,  the  occurrence  of  maxima  of  nucleation  may  in  a  large  measure 
be  obviated  by  distributing  the  radium  along  the  axial  tube. 

45.  The  same.  Preliminary  data. — To  test  the  efficiency  of  the  fog 
chamber  it  is  sufficient  to  make  a  preliminary  measurement  of  Thom- 
son's e.  Let  the  radii  of  the  electrical  condenser  be  R±  and  R2,  its  length 


STANDARDIZATION    OF    FOG    CHAMBER. 


57 


7;  let  C  (electrostatic  units)  be  the  capacity  of  the  electric  system,  con- 
denser, and  electrometer,  together  with  such  auxiliary  capacity  as  may 
be  inserted  to  get  a  leakage  of  proper  value.  Let  U  be  the  efficient* 
velocity  of  the  ions,  positive  or  negative  as  the  case  may  be,  in  a  field  of 
i  volt  per  centimeter,  V  the  voltage  and  V  the  change  of  voltage  per 
second.  Finally,  let  TV  be  the  nucleation  caught  when  the  identical 
condenser  core  is  placed  in  the  fog  chamber.  Then  for  the  cylindrical 
condenser  (if  natural  logarithms  be  taken) , 

ClnRJR9  V 
~  6oonlUN  V 

If  V  is  small  enough  to  keep  V/V  constant,  the  curves  show  this  at 
once.  Rough  tests,  using  the  old  data  of  my  fog  chamber,  led  to  values 
about  as  shown  in  table  20,  where  the  irregularities  are  in  the  electro- 
meter, due  it  was  supposed  to  the  connecting  wires,  which  were  not  at 
the  time  surrounded  by  earthed  pipes.  It  has  been  assumed  that  relative 
ions  only  are  caught  in  the  fog  chamber  and  that  a  negative  current  only 
is  observed.  The  e  so  found  is  too  large. 

TABLE  20.  —  Preliminary  values  of  e.    Wires  not  surrounded  by  pipes. 
c_ClnRl/R2  V/V 

C=i3o;    £7=1.87  cm. /sec.  (neg.  ions);    V<o.5  volt;  field  0.7  volt/cm.;  7V=2io,ooo 
per  cm3  (neg.  ions);    2^  =  2.1  cm.;    2R2  —  o.62  cm.;    /=i8.2  cm. 


V/V 

eXio10 

V/V 

<?Xio10 

V/V 

eXio10 

0.049 

56 
65 

71 

.... 

0.054 
62 
56 
50 

.... 

0.056 
68 
67 
65 
67 

.... 

.060 

*o.05 

7-3 
6-4 

0.56 

6-9 

.065 

8.0 

*  Same  with  N=  185,000  per  cm3  (neg.  ions). 

46.  The  same.  Wires  surrounded  by  earthed  pipes. — In  order  to 
make  use  of  the  high  sensitiveness  of  the  Dolezalek  electrometer,  the 
wires  were  now  surrounded,  so  far  as  possible,  with  pipes  of  galvanized 
iron,  2  inches  in  diameter,  put  to  earth.  Under  these  circumstances  there 
was  less  irregularity,  though  the  current  still  continued  to  be  far  from 
proportional  to  the  voltage,  even  for  low  values  of  the  latter.  It  will 
not,  therefore,  be  worth  while  to  give  a  detailed  account  of  V/V,  and  the 
mean  value  for  a  field  of  i  volt  per  centimeter  was  taken,  as  found  from 

*If  one  shell  of  the  condenser  is  put  to  earth,  positive  or  negative  currents  only  are 
measured  and  not  the  whole  current. 


58        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


five  independent  series  of  measurements  of  the  fall  of  the  potential  of 
the  core  per  second.  The  following  is  the  summary,  referring  to  the 
negative  current,  where  C  is  136  cm.,  £7=1.87  cm. /sec.,  P=i8.8  cm., 
2^=2.1  cm.,  2^2  =  0.62  cm. 


V 

Field. 

v/v 

(Negative 
ions) 

eXio10 

N 

Volt 

Volt/  cm. 

Els.  units. 

0.7 

i 

0.04 

150,000 

6.6 

•9 

I  .  2 

.14 

570,000 

5-9 

When  the  condenser  was  disconnected  there  was  no  leakage,  showing 
the  piping  to  be  nearly  free  from  such  currents  as  might  result  from 
irregular  penetration  of  the  gamma  rays.  The  approach  of  the  final 
values  of  e  to  those  currently  in  use  is  no  closer  than  before.  It  has  again 
been  assumed  that  negative  ions  only  have  been  caught  in  the  fog  cham- 
ber, and  that  a  negative  current  alone  is  in  question  when  the  core  (con- 
nected with  the  electrometer)  is  charged  positively  and  the  shell  of  the 
condenser  is  put  to  earth. 

47.  Conclusion. — The  values  of  e  obtained  under  widely  varied  con- 
ditions in  the  present  rough  experiments,  are  of  the  same  order  and  to 
this  extent  show  that  the  present  method  is  not  unworthy  of  develop- 
ment, with  a  view  to  the  further  measurements  of  this  important  con- 
stant. For  this  purpose  I  have  been  at  work  on  a  redetermination  of  the 
nucleation  values  of  the  coronas  (see  Chapter  II),  using  as  a  source  of 
light  the  virtually  monochromatic  mercury  lamp.  This  is  sufficiently 
intense  and  the  coronas  admit  of  a  more  definite  optical  interpretation. 

All  of  the  e  values  are  too  high,  however,  when  it  is  assumed  that  a 
negative  current  only  is  in  question  and  that  negative  ions  only  are 
caught.  The  reason  for  this  high  value  of  e  is  probably  referable  to  the 
aluminum-brass  condenser,  which  contains  an  electromotive  force  not 
allowed  for  nor  eliminated  by  commutation.  Such  a  case  would  modify 
the  ratio  V/V  in  the  above  results  by  changing  the  zero-point  of  the 
electrometer.  The  experiments  were  abandoned  at  this  point  owing  to 
the  dampness  of  the  summer  season.  They  will  be  resumed  in  Chapter  V. 


STANDARDIZATION    OF    FOG    CHAMBER.  59 

THOMSON'S  CONSTANT  e,  EXPRESSED  IN  TERMS  OF  THE    DECAY  CON- 
STANT OF  IONS,  WITHIN  THE  FOG  CHAMBER. 

48.  Introductory. — In  the  last  paper*  an  account  is  given  of   certain 
tentative  experiments  to  determine  Thomson's  electron,  by  aid  of  the 
fog  chamber  and  a  separate  well-leaded  cylindrical  electrical  condenser. 
The  results  obtained  were  in  keeping  with  the  accepted  values.    It  was 
presumed  that  the  constants  of  coronas  are  determinable  from  purely 
optical   considerations   of   diffraction   and   interference,   and   that   the 
accuracy  of  the  method  may  be  enhanced  by  using  the  mercury  lamp  as  a 
source  of  light  for  the  coronas.    There  was,  however,  one  grave  misgiving, 
inasmuch  as  the  distribution  of  ionization  within  the  fog  chamber  varies 
in  marked  degree  from  place  to  place  for  any  given  position  of  a  sealed 
radium  tube,  and  that  the  mean  value  assumed  was  in  a  measure  gratui- 
tous.   The  results  seen  in  the  fog  chamber  are  a  complication  of  the  effects 
of  primary  and  secondary  radiations,  together  with  a  very  marked  ex- 
haustion displacement  of  the  ions.     The  maximum  ionization  (Chapter 
III)  does  not  coincide,  as  a  rule,  with  the  position  of  the  radium,  and  there 
is  no  reason  why  the  ionization  in  the  fog  chamber  should  be  quite 
identical  with  the  ionization  produced  by  the  same  radium  tube  in  the 
electrical  condenser,  unless  both  are  one  and  the  same  apparatus.    This  is 
the  case  in  the  experiments  of  the  present  paper.    The  results  also  show 
that  the  same  method  may  be  applied  under  the  circumstances  of  the 
last  paper,  where  e  was  obtained  in  terms  of  the  velocities  of  the  ions. 

49.  The  electrical  condenser  fog  chamber. — It  is  therefore  necessary 
to  make  a  fog  chamber  itself  the  electrical  condenser,  and  this  is  easily 
done,  if  the  chamber  is  cylindrical,  by  installing  a  tubular  core  of  alumi- 
num closed  in  the  inside  of  the  chamber  and  running  axially  from  end 
to  end,  as  in  fig.  18.    This  core  is  charged  to  a  definite  potential  and  made 
the  inner  surface  of  the  condenser,  while  the  scrupulously  clean  inner 
wall  of  the  glass  chamber  (to  which  water  adheres  evenly)  is  the  outer 
surface  and  put  to  earth.    Finally,  the  radium,  contained  in  small  sealed 
tubelets  of  aluminum,  is  placed  within  the  length  of  the  axial  aluminum 
tube  or  core  in  such  a  way  as  to  make  the  ionization  within  the  fog 
chamber  uniform — a  condition  vouched  for  in  case  of  the  occurrence  of 
uniform  coronas  on  exhaustion,  from  end  to  end  of  the  chamber. 

There  are  thus  three  currents  to  be  determined: 

(i)  The  conduction  current  due  to  inevitable  leakage  between  the 
condenser  surfaces.  This  is  made  a  minimum  and  nearly  negligible  in 
value  by  keeping  the  aluminum  core  out  of  the  condenser  when  not  in 
use  and  by  sheathing  it  with  an  annular  air-space  beyond  the  condenser. 
It  is  found  experimentally  by  direct  measurement  in  the  absence  of 
radium. 

*C.  Barus:    Am.  Journ.  Sci.,  xxvi,  pp.  87-90,  1908. 


60        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

(2)  The  current  due  to  the  ionization  of  the  room  air  near  the  fog 
chamber  and  on  the  outside  of  it,  due  to  gamma  rays.    This  is  made  a 
minimum  by  allowing  the  thin  wire  communicating  with  the  electro- 
meter to  run  axially  away  from  the  fog  chamber,  for  the  gamma  rays, 
in  spite  of  their  penetrating  powers,  are  quickly  reduced  by  distance. 
The  current  is  found  in  the  presence  of  radium  within  the  axial  tube  by 
leaving  all  adjustments  identically  in  place,  but  breaking  the  metallic 
connection  between  the  aluminum  core  and  the  electroscope,  etc.,  by  a 
hard  rubber  insulator.     If  an  auxiliary  condenser  is  used,  the  measure- 
ment (i)  must  be  made  without  it,  as  otherwise  its  leak  would  be  counted 
twice.     Fortunately  the  conduction  current  is  quite  negligible. 

(3)  The  current  due  to  ionization  within  the  fog  chamber.     This  is 
found  by  deducting  from  the  total  current  found  on  connecting  the 
charged  aluminum  core  and  the  electrometer  the  two  preceding  currents. 

50.  Auxiliary  condenser.  —  To  vary  the  experiments  to  the  extent 
that  different  speeds  of  leakage  may  be  obtained,  as  well  as  to  find  the 
capacities  of  the  electrometer  and  fog  chamber,  an  auxiliary  condenser 
must  be  inserted  as  a  part  of  the  electroscope.  This  condenser  consisted 
in  the  present  experiments  of  two  plates  of  brass,  having  an  area  of  315 
sq.  cm.,  and  usually  kept  at  a  distance  of  0.32  cm.  apart  by  ou  trigged 
feet  of  hard  rubber,  which  stood  on  a  plate  of  glass.  By  putting  small 
glass  plates  under  these  feet  the  capacity  could  be  varied  at  pleasure. 
The  usual  equation  was  corrected  by  aid  of  the  factor 


where  a  is  the  area,  d  the  distance  apart,  and  d  the  thickness  of  the  plate 
of  the  auxiliary  condenser.  Naturally  a  guard  ring  condenser  would 
have  been  preferable  for  standardization,  but  none  was  at  hand. 

To  determine  the  very  small  capacity  C  of  the  electroscope-fog-cham- 
ber,  two  successive  full  charges  from  the  lighting  circuit,  at  a  potential  V  = 
250  volts,  were  in  turn  imparted  from  C  to  the  auxiliary  condenser  of 
capacity  C'  .  If  V"  be  the  potential  observed  after  these  two  charges  and 
S  =  V"I  (V-V"),  C  =  C'S/(i  +  vVfS).  It  is  curious  that  this  method 
of  successive  charges  leads  to  involved  cubic,  quartic,  quintic  equations, 
etc.,  which  follow  no  simple  rule.  The  ratios  R  of  the  potentials,  after 
four  and  after  two  charges  R  =  V""  /V"  is,  however,  still  available 


for  if  r  =  C'/C,thenr=(R-i)i  +  \/i  +  (2-R)/(R-i/(2-R).    Apart 

from  these  complications,  the  large  deflections  obtainable  after  many 
successive  charges  would,  in  the  absence  of  conduction  leakage  in  the 
condensers,  make  this  method  very  satisfactory. 

In  the  definite  measurements,  however,  almost  the  whole  capacity 
may  be  placed  in  the  auxiliary  condenser,  so  that  the  capacities  of  the 


STANDARDIZATION    OF    FOG    CHAMBER.  6l 

electrometer  and  fog  chamber  are  of  small  importance.      Ratios  of 
C//C  =  86/i7,  30/17,  20/17,  and  others,  were  tried. 

51.  Method.  —  In  the  preceding  paper  the  value  of  e  found  was  ulti- 
mately dependent  upon  the  velocity  of  the  ions  in  the  unit  electric  field. 
In  the  present  experiments  a  value  will  be  found,  based  on  the  decay 
constant  b  =  i  .  i  X  io~6,  of  the  ions.  This  method  has  the  advantage  that 
large-core  potentials  are  admissable  in  the  electrical  condenser,  so  that 
an  ordinary  graduated  Exner  electroscope  suffices  for  the  measurement 
of  current.  The  small  capacities  of  the  instrument  make  it  necessary  to 
insert  an  auxiliary  condenser,  as  otherwise  the  discharges  are  too  rapid 
for  trustworthiness. 

If  a  is  the  number  of  ions  produced  per  second  per  cubic  centimeter 
by  the  radium  within  the  condenser  core,  n  the  number  of  nuclei  per 
cubic  centimeter  in  general,  and  N  the  number  of  nuclei  (ions)  found 
when  the  core  is  free  from  charge,  dn/dt  —  a  —  bn2  =  o,  if  n  =  N.  Again,  if  n 
is  the  number  of  nuclei  found  when  the  core  is  charged  and  i  the  cor- 
rected current  observed,  e  Thomson's  constant,  and  v  the  effective  volume 
of  the  fog-chamber  condenser, 


n2)-i/ev-=o  (i) 

Hence  if  the  capacity  of  the  system  is  C  and  V,  the  corrected  fall  of 
potential  per  second 

e  =  CV/(bv(N*-n*)}  (2) 

Usually  V  is  measured  in  volts,  so  that  V/$oo  replaces  V  in  the  equation. 
It  is  obvious  that  V  must  be  large  enough  to  keep  the  current  V  constant 
and  the  observations  always  show  this  at  once. 

If  equation  (i)  is  multiplied  by  J  throughout  it  will  express  the  case 
for  the  negative  ions  alone  and  the  negative  current  alone.  Hence 
equation  (2)  is  at  once  applicable  here. 

52.  Data  disregarding  external  gamma  rays.  —  By  the  aluminum-foil 
electroscope  it  was  made  convenient  to  use  the  high  potentials  of  the 
electric-lighting  circuit  (about  250  volts)  for  charging. 

The  number  of  nuclei  (ions)  found  in  the  presence  of  the  radium  tube- 
lets  and  in  the  exhausted  fog  chamber  free  from  charge  at  its  central  core 
was  N  =  474,  ooo.  The  number  of  nuclei  found  in  the  exhausted  fog 
chamber  when  the  core  was  charged  250  volts  was  n'  =  82,5oo.  Hence 
about  391,000  vanished  in  the  presence  of  the  electrical  current,  the 
original  apertures  of  the  coronas  being  reduced  from  about  22°  to  13°. 
The  drop  of  pressure,  §p/p  =  o.^o  nearly,  was  taken  high  enough  to  catch 
all  the  available  ions,  but  not  so  high  as  to  catch  the  vapor  nuclei  of  dust- 
free  wet  air. 


62        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


The  amount  of  exhaustion  was  equivalent  to  the  volume  ratio  vjv=* 
1.29.  Thus  the  number  of  ions  in  the  fog  chamber  at  atmospheric  pres- 
sure was  N  —  611,000  per  cubic  centimeter  for  the  uncharged  core. 

TABLE  21.  —  Fall  of  potential  and  currents.     V'  conduction  leakage;   V"  due  to  presence 
of  radium.    Wires  not  piped.    Four-second  intervals  between  observations. 


V 

V' 

V" 

V" 

V" 

V" 

V  =  3.0  volt/sec.  ;  C=io3. 

V  =  5.  8  volt/sec.;  C  =  47. 

250 
247 

237 
226 
216 
205 
195 

1.6 

2.6 
2.6 
2.6 
2.6 

250 
230 
206 

183 
1  60 
140 

122 

5-5 
5-9 
5-7 
5-4 

249 
229 
205 
1  80 
155 
135 
no 

90 

5-5 
6.1 

6.2 

5-6 
5-6 
5-6 

5-6 

5-8 

V  =  6.  4  volt/sec.  ;  C  =  4y. 

7=12.1  volt/sec.  ;  C  =  ij. 

250 
236 

221 
207 

195 

182 

168 

3-6 

3-4 

3-2 

3-2 

250 

216 

175 
133 

99 

9-4 
10.4 

9-5 

249 
209 

153 
103 

12.0 
13.2 
10.4 

12.0 
13.0 
IO.9 

12.3 
12.7 

9.8 

3-4 

249 
207 

153 
103 

249 
205 

151 
103 

12.  I 

The  value  of  6=i.iXio6  is  taken  from  Professor  Rutherford's  book. 
The  source  of  light  for  the  coronas  is  part  of  a  Welsbach  mantle,  as  usual, 
and  the  old  constants  of  coronas  were  used,  since  it  is  a  part  of  the  purpose 
of  this  paper  to  test  those  constants.  The  volume  of  the  fog  chamber  was 
estimated  at  51,000  c.  cm.  In  the  first  experiments  the  effect  of  the 
gamma  rays  penetrating  into  the  air  on  the  outside  of  the  fog  chamber 
was  neglected  and  the  data,  summarized  from  table  21 ,  on  using  different 
condensers,  were  as  follows,  all  data  being  given  in  electrostatic  units. 
C  denotes  the  capacity  of  the  system,  V  the  drop  of  potential  per  second, 
i  the  corrected  current  passing  through  the  condenser-fog-chamber. 


C 

FXio3 

z'Xio2 

eXio10 

103 

10 

103 

5-i 

47 

21 

101 

5-o 

47 

19 

92 

4-5 

17 

40 

70 

3-4 

STANDARDIZATION    OF    FOG    CHAMBER. 


The  last  observation  being  made  without  an  auxiliary  condenser.  The 
current  i  was  quite  constant  throughout  the  voltage  interval  (near  250 
volts)  of  observation.  Hence  the  effect  of  gamma-ray  penetration  has 
seriously  increased  the  leakage,  and  e  therefore  appears  too  large,  except 
in  the  last  observation,  where  i  is  probably  no  longer  measureable. 

53.  Further  data. — In  the  following  experiments  the  effect  of  the 
external  gamma  rays  was  eliminated  as  specified  in  section  49.  The  con- 
duction current  was  usually  quite  negligible.  The  nucleations  observed 
in  the  exhausted  fog  chamber  were  ^  =  82,000  and  iV  =  506,000,  when 
the  core  was  charged  and  uncharged,  respectively.  The  exhaustion  was 
again  equivalent  to  a  volume  increase  of  vl/v=i.2g.  Hence  in  the  fog 
chamber  full  of  air  the  respective  nucleations  are  N  =  65  3,000  and  n  = 
106,000,  whence  Ar2  — n2  =  4i5X  io9.  The  drop  of  pressure  dp/p  =  o.^o 
was  about  the  same  as  before. 

TABLE  22.  — Fall  of  potential  and  currents.     V  in  the  presence  of  radium;    V"  due  to 
f  rays;    V      leakage  due  to  conduction;     4-sec.  intervals.    Wires  in  earthed  pipes. 


V 

V* 

V 

V" 

V" 

ynr 

V 

V* 

V" 

V" 

y/ff 

V=  2.  24  volt/sec.;  C=iO3. 

F  =  5.  88  volt/sec.;  C  =  37. 

245 
232 
218 
203 
189 
T74 
157 
141 

3-4 
3-6 
3-6 
3-6 
3-9 

3-7 

244 
236 
232 
228 

221 
217 
2O9 

•5 

.0 

•4 
•  4 

•5 

^38 

247 
243 
240 

237 
235 
232 
230 

0.9 
.8 
.6 
.6 
.6 
•9 

240 
204 
175 
139 

8.1 
8.1 
8.1 

241 
231 

221 
21  I 
205 

195 

I87 

2-5 
2.5 

2.0 
2.0 
2.  2 
2.  I 

.6 

•1 

•  4 
.6 

•5 

8.1 

2.22 

.48 

V—  i  o.o  volt/sec.  ;  C=ij. 

V"  =  5-i5  volt/sec.;  C  =  4y. 

248 
1  80 

121 
70 

248 

187 
130 

74 

15-9 
13-8 
14.8 

14-7 
14-4 

245 
226 
209 
191 
175 

4-5 

4-4 
4-3 
3-9 

0.21 
•17 
•19 

245 
217 
189 
161 
J34 

7.0 
7-o 
6-9 

244 
232 
225 
217 
2O9 
203 

195 
190 

i-9 

2.0 

1.8 
1.8 
1.6 

.... 

•  4 
.  i 

.8 
•3 

.  2 
.O 

•19 

6-97 

4-4 

1.82 

•13 

The  electrical  measurements,  if  all  data  are  given  in  electrostatic  units, 
may  be  summarized  from  the  data  in  table  22,  as  follows: 


c 

FXio3 

iXio2 

eXio10 

103 

7-5 

77 

3-3 

47 

17.2 

81 

3-5 

37 

19.6 

72 

3-i 

17 

33 

58 

2-5 

64        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

Thus,  with  a  correction  for  the  external  gamma  radiation,  the  data  for 
e  show  reasonable  values,  in  spite  of  the  simplicity  of  the  experiment. 
It  follows,  therefore,  even  in  the  case  of  such  large  numbers  of  ions  as 
occur  in  these  experiments  (over  500,000),  that  the  constants  of  coronas 
used  heretofore  are  substantially  correct.  In  case  of  the  last  value 
£Xio10=2.5,  for  the  small  capacities  of  17  cm.,  the  aluminum  leaves 
on  the  electroscope  converge  too  rapidly  for  measurement,  so  that  the 
air  resistance  may  have  produced  an  appreciable  discrepancy.  Hence 
both  i  and  e  are  too  small.  No  refinement  has  been  attempted  in  these 
experiments,  their  chief  purpose  being  to  test  the  standardization  of  the 
fog  chamber  in  terms  of  coronas  and  the  degree  to  which  positive  and 
negative  ions  may  be  caught  even  at  very  high  nucleation.  One  may  note 
in  conclusion  that  the  currents  ^'=77  electrostatic  units  or  2.6 Xio10 
amperes  are  already  quite  within  the  reach  of  the  sensitive  galvanometer. 


CHAPTER  V. 

THE  ELECTRON  METHOD  OF  STANDARDIZING  THE  CORONAS  OF  CLOUDY 
CONDENSATION,  IN  TERMS  OF  THE  VELOCITIES  OF  THE  IONS. 

54.  Introductory. — In  the  following  experiments  I  have  returned  to 
the  measurements*  of  N  in  terms  of  e  and  the  velocities  of  the  ions, 
Chapter  IV,  modifying  the  method  by  using  the  cylindrical  fog  chamber 
both  as  an  electrical  condenser  for  the  measurement  of  current,  as  well 
as  for  the  specification  of  the  number  of  ions  in  action  by  aid  of  the 
coronas  of  cloudy  condensation.     It  is  to  be  assumed  that  negative  ions 
only  are  caught  in  the  fog  chamber. 

55.  Apparatus   (fig.    19.) — This  consists  of  a  cylinder  of  glass  CF, 
about  45  cm.  long,  13.4  cm.  internal  diameter,  closed  at  one  end  F,  and 
provided  with  a  brass  cap  C  with  exhaust  E  and  influx  attachments  7, 
in  the  usual  way.    There  is  a  layer  of  water  w  at  the  bottom.    The  glass 
must  be  scrupulously  clean  within,  and  this  is  best  secured  by  scouring 
with  a  probang  of  soft  rubber  under  water,  until  the  water  adheres  as  an 
even  film  on  shaking.    The  fog  chamber  is  put  to  earth. 


i   C 

4!   <r                   V                     'T         j: 

t 

fW 

' 

P                                                                    £ 

-r 

fff> 


FIG.  19. — Electrical  condenser  and  fog  chamber  combined,  showing  the  dis- 
position of  the  auxiliary  condensers  Cr  and  C",  the  Clarke  cell  S,  and  the 
electrometer  K,  diagrammatically.  Earthed  wires  are  shown  at  e. 

The  end  F  is  perforated  at  h  to  receive  the  aluminum  tube  #',  closed 
at  t'  and  open  at  t,  40  cm.  long  and  0.64  cm.  external  diameter.  Sealed 
tubelets  of  radium  rr  may  be  placed  at  intervals  within  this  tube  to  ionize 
the  surrounding  wet  air.  The  walls  being  about  o.i  cm.  thick,  ft  and  y 


*Amer.  Journ.  Sci.,  xxvi,  1908,  p.  87;  idem.,  p.  324. 


66        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

rays  are  wholly  in  question.  Neither  emanation  nor  a  rays  escaped  the 
double  thickness  of  aluminum.  The  tube  it'  is  grasped  at  t  by  a  sheath  of 
hard  rubber  with  an  annular  air-space  and  fixed  in  place  by  a  rubber 
cork.  If  care  be  taken  to  keep  the  tube  in  dry  air  except  when  in  use, 
there  is  no  conduction  leakage  of  consequence. 

The  end  t,  moreover,  is  placed  in  connection  with  a  Dolezalek  electro- 
meter, by  aid  of  a  thin  wire  running  axially  within  an  earthed  tin  drain 
pipe  and  away  from  the  fog  chamber,  to  escape  the  action  of  y  rays  as 
much  as  possible.  In  fact,  their  combined  effect  does  not  exceed  2  per 
cent  and  is  determined  in  special  measurements. 

The  keys  to  the  electrometer  were  all  placed  on  pillars  of  hard  rubber 
and  actuated  by  long  wooden  rods  from  a  distance.  So  far  as  possible 
the  electrical  wires  of  the  room  were  surrounded  by  earthed  pipes,  but 
it  was  not  practicable  to  carry  this  out  completely,  so  that  a  method  of 
correction  appears  in  the  tables  below.  Even  when  the  electric-lighting 
circuit  was  completely  cut  out  the  electrostatic  drift  in  question,  supposed 
to  be  due  to  this  cause,  remained.  It  was  afterwards  found  that  the 
source  of  drift  was  due  to  an  imperfection  in  the  electrometer,  but  that 
it  could  be  eliminated  by  commutation,  as  was  done. 

The  measurements  were  standardized  and  the  electric  system  charged 
by  a  Carhart-Clarke  cell.  The  radium  tubelets  used  were  as  follows: 
I,  loomg.,  strength  1  0,000  X  ;  II,  iomg.,  strength  2  00,000  X  ;  III,  100 
mg.,  strength  io,oooX;  IV,  100  mg.,  strength  7,000X1  V,  100  mg., 
strength  20,000  X- 

56.  Auxiliary  electrical  condensers.  —  To  give  the  fall  of  potential 
a  suitably  small  value  relatively  to  the  period  of  the  damped  drop  of  the 
needle  a  number  of  auxiliary  condensers  (fig.  19),  are  needed.  It  suffices, 
however,  to  measure  three  capacities,  viz:  (i)  that  of  the  cored  fog 
chamber  alone,  c\  (2)  that  of  a  relatively  large  auxiliary  condenser, 
including  the  electrometer,  the  piped  wires,  and  the  fog  chamber,  C"  +  c\ 
(3)  that  of  a  standard  condenser  Cf  for  reference. 

In  the  present  paper  Cr  was  computed  by  the  equation 


A 


r> 

C  =  —  ,—T 

\/nA  d2  d 


d+d'\ 
m  —  —  1 


where  A  is  the  area,  d  the  distance  apart,  and  d'  the  thickness  of  the  brass 
plates.    Since  A  is  equal  315  sq.  cm.,  d  =  0.082  cm.,  ^'  =  0.67  cm., 

C'  =  305.6(1  +  0.0784)  =  330  cm. 

This  value  will  suffice  for  the  present  purposes,  though  it  needs  further 
correction  by  comparison  with  a  standard  condenser  not  now  at  hand. 


ELECTRON    METHOD    OF    STANDARDIZING    CORONAS.  67 

A  special  key  was  provided  whereby  C'  could  be  switched  into  the 
electrometer  system  or  out  of  it  and  put  to  earth.  Hence  in  a  series  of 
successive  discharges 

(C"  +  c)V=  (C"  +  C'  +  c)  V  (C"  +  c)V'  =  (C"  +  C'  +  c)  V",  etc.  , 

so  that  for  n  discharges,  if  the  residual  potential  is  Vn 


from  which  the  total  capacity  C  —  C"  +  C'  +  c  is  determinable  in  terms 
of  C.  The  results  were 

Positive  charge  ........  C"+  C'+  c=»  1445         1443         1422 

Negative  charge  .......  C"+  C'+  c«=          1482         1480 

Mean  ................  .  .......  C=  1459 

the  experiments  alternating  from  positive  to  negative  charge,  because 
of  the  marked  drift  by  the  electrometer  system  when  isolated  from  the 
cell,  as  already  specified.  To  measure  the  small  capacities  c  of  the  fog 
chamber,  the  same  method  with  ten  discharges  suffices,  if  C"  is  excluded 
and  C'  retained.  Thus  the  data  were  successively  found, 

-f  Charge  ............  c=n.8  12.4  12.2  12.9 

—  Charge  ............  c=io.8  10.4  n.i  11.5 

Mean  .............  c=n.3  11.4  n.6  11.2 

eliminating  the  drift  in  the  final  mean  £=11.4. 

Since  the  capacity  c  in  terms  of  the  effective  internal  radius  R%  and 
external  radius  Rl  and  lengths  /  of  the  cylindrical  condenser  may  be 
written 

i  '        R,  i 

7  log  -£ 


2X2. 

the  constant  c  furnishes  a  mean  value  for  the  factor  on  the  left.  The 
ratio  of  4.6^  to  the  measured  value  of  (log  R/RJ/l  was  0.568,  a  reduction 
factor  used  throughout  the  tables  below. 

57.  Method  pursued. — If  C  is  equal  to  C"-f  C'  +  c  we  may  write  the 
equation  for  the  negative  ionization  N  (positive  charge) 

ClnRJR,  d(lnV)       d(\nV) 


600  TT  he       dt  dt 

where  Rlt  Rz,  and  /  are  the  effective  radii  and  length  of  the  condenser, 
io10£  =  3.4,  #=1.51  cm. /sec.,  and  11=1.37  cm. /sec.,  the  velocity  of  the 
negative  and  positive  ions  in  the  unit  field,  volt/cm.,  and  in  case  of  moist 
air.  The  factor  (InR^/R^/l  is  replaced  by  C/2,  as  specified  in  section  56, 


68        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

which  must  here  be  regarded  as  an  adequate  correction  for  the  ends  and 
the  imperfect  cylindricity  of  the  condenser  fog  chamber.  Similarly  the 
equation  for  the  positive  ionization  is  (negative  charge) 

ClnRJR,   d(lnV)      ,d(lnV) 

l\    =  ~ ; : =  K 


600  nine         dt  dt 

and  the  total  ionization  is  therefore  N+N'. 

The  experiments  below  will  show  that  even  if  the  fog  chamber  is  put  to 
earth  there  is  a  drift  towards  negative  potential  sufficiently  steady  as 
to  be  eliminated  in  the  mean  results. 

The  drift  is  due  to  a  high  permanent  voltage  which  has  its  seat  in  the 
electrometer  and  is  not  due  to  the  lighting  circuit  of  the  building,  for, 
even  when  this  circuit  is  cut  out,  the  effect  remains  with  undiminished 
intensity.  It  will  appear  in  Chapter  VI  that  in  the  absence  of  radium  and 
of  initial  charge  in  the  condenser  the  equation  Ia  =  CV  0,  where  Va  for 
any  given  ionization  is  a  constant  quantity,  of  the  same  sign  as  the 
voltage  of  the  needle,  applies  very  closely  within  the  limits  of  measureable 
I^0  values.  Hence  in  the  presence  of  radium  in  the  core  of  the  cylindrical 
fog  chamber  and  a  positive  charge 

/0+6oo  TT  IVNev/lnRJR^C  V 
Thus  in  this  case 

'VN  =  «d(V  -  Va)  /dt         -  V'N'  =  K'd(-V-  Va)  /dt 
and  for  the  same  V  =  V  ,  to  a  first  degree  of  approximation, 


numerically,  as  before.    If  the  equation  for  N  is  integrated,  and  N/*  =  K, 
since  Ia  =  CVa,  Va  being  intrinsically  negative  for  a  negative  needle, 

V  =  e-Kt(VQ-VJK)  +  VaK         V  =  6-™(V'Q+  VJK'}  -  VJK' 

where  V0  and  V'0  are  the  initial  positive  and  negative  potentials.    Both 
of  these  are  of  the  form 


where  k  is  a  constant,  considered  in  the  next  chapter.    If  k  —  o,  as  in  the 

y 
present  case,  and  V  =  V,  the  correction  would  be  —±(it  -  K  )  ,  which  shows 

that  large  values  of  V  only  are  admissible. 


ELECTRON    METHOD    OF    STANDARDIZING    CORONAS. 


69 


58.  Data.  High  ionization.  Currents. — The  following  tables  con- 
tain the  mean  potentials  V,  the  positive  and  negative  logarithmic  cur- 
rents d(log  V)/dt  (apart  from  the  constant),  the  apparent  nucleation  N 
positive  and  N'  negative,  computed  from  these  data  and  the  additional 
information  at  the  head  of  the  tables.  In  most  of  the  cases  the  corre- 
sponding logarithmic  currents  due  to  rays  outside  the  fog  chamber  was 
carefully  measured  in  the  same  units  by  placing  a  short  hard  rubber  rod 
between  the  end  /  of  the  aluminum  tube  (fig.  1 9)  and  the  wire  leading  to 
the  electrometer.  This  cuts  out  the  fog  chamber,  but  leaves  the  whole 
remaining  circuit  undisturbed. 

Similarly  the  leak  value  of  d  (log  V)  /dt  in  the  absence  of  radium  and  due 
to  mere  conduction  of  moist  parts  is  always  quite  negligible.  Thus  in  the 
first  part  of  table  23,  for  relative  logarithmic  currents  in  the  order  of 
0.035,  the  y  raY  effect  is  o.ooio,  the  conduction  leakage  smaller  than 
o.oooi.  The  other  extreme,  i.  e.,  the  value  of  d(\og  V)/dt  for  the  freely 
falling  needle  is  about  o.i  in  the  same  units.  Hence  it  follows  that  in  the 
first  part  of  table  23  the  needle  falls  faster  than  would  be  quite  trust- 
worthy, therefore  the  auxiliary  capacity  selected  is  too  small. 

Moreover,  the  negative  current  only  is  here  measured,  as  the  indis- 
pensable need  of  measuring  both  currents  was  not  then  apparent.  Hence 
in  the  second  part  of  table  23  the  measurement  of  both  currents  is  under- 
taken. At  the  same  time  the  capacity  of  the  condenser  has  been  increased 
to  give  the  needle  the  necessary  slow  descent.  The  time  interval  between 
observations  for  V  is  4  seconds  in  both  parts. 

TABLE  23.  —  Number  of  ions  per  cm3.  Cylindrical  condenser  fog  chamber.  Capacity 
of  system:  small  auxiliary  condenser,  330  cm.;  electrometer  and  wire,  69  cm.;  fog 
chamber,  11.400.;  total,  410  cm.  Fog  chamber:  glass  2^  =  13. 4  cm.;  aluminum 
core,  2^2  =  0.635  cm. ;  £  =  39. 5  cm.  Velocity  of  ions:  u=  1.37  cm./sec. ;  ^  =  1.51  cm. /sec. 
in  field  of  volt/sec;  e  =  3.4Xio~10.  Current  due  to  prays  without:  d  (log  V)/dt  — 
o.ooi ;  current  due  to  conduction  leakage  d  (log  V)/dt  =  0.000081.  Accelerated  free 
fall  of  needle,  d  (log  V)/dt  =  o.o6  to  o.  16  for  corresponding  deflections.  Time  interval 
4  sec.  Radium  I  +  II  +  III  +  IV  +  IV'  +  V.  *  =  76Xio6.  Cm.  of  scale  equivalent  to 
0.0585  volt. 


V 

d  (log  V)/dt 
Xio4 

NXio-3 
corrected. 

V 

d(\ogV)/dt 
Xio4 

AT  Xio-3 
corrected. 

I  Charge  +. 

I  Charge  H  —  Continued. 

1.32 

I  .  IO 

•83 
-58 

H5 
262 

355 
445 

621 
1130 
1530 
1910 

0-37 
.19 
.06 

5i8 
1360 
1118 

2230 
5870 
4850 

70        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

TABLE  23 — Continued. 

The  same,  with  larger  auxiliary  condensers:  Capacity  of  fog  chamber,  11.4  cm.; 
C",  1049 cm.;  C',  330 cm. ;  wires  and  electrometer,  69  cm. ;  total,  1459  cm.  Current 
due  to  gamma-rays  without  d  (log  V)/dt  =  o.ooo2i  (pos.  ch.)  to  0.00022  (neg.  ch.). 
Time  interval  4  sec.  Radium  I-V.  Charges  positive  and  negative.  Positive 
charge  K  =  289X10";  cm.  of  scale  equivalent  to  0.0608  volt.  Negative  charge 
*'=* 319X10°;  cm.  of  scale  equivalent  to  0.0613  volt. 


V 

d  (log  V)/dt 
Xio4 

ATXio-8 
corrected. 

V 

d  (log  V)/dt 
Xio* 

NXio-8 
corrected. 

II.  Charge-. 

III.  Charge  -K 

•43 

4 

74 

•42 

9 

138 

.42 

19 

323 

•39 

33 

503 

•39 

3i 

525 

•34 

54 

827 

•35 

37 

625 

.26 

68 

1040 

•3° 

4i 

694 

.18 

86 

i3H 

•25 

37 

625 

.10 

72 

IIO2 

.21 

35 

599 

•03 

7i 

1092 

•17 

39 

678 

•97 

75 

1150 

•13 

35 

594 

.91 

66 

IOI2 

.09 

36 

610 

•85 

78 

1192 

.06 

34 

583 

•79 

84 

1288 

•03 

32 

54i 

•73 

72 

1  102 

.00 

30 

509 

.68 

88 

1346 

•97 

3i 

525 

•63 

84 

1293 

•94 

28 

472 

•58 

9i 

1399 

.92 

32 

54i 

•53 

87 

1330 

.89 

33 

567 

•49 

94 

1447 

•87 

27 

456 

.84 

3i 

530 

.... 

.82 

32 

54i 

.... 

.80 

21 

355 

•37 

107 

1643 

•  78 

34 

578 

•34 

98 

1505 

.76 

26 

440 

•30 

!3J 

2OI4 

•74 

27 

456 

-27 

122 

1876 

.72 

18 

302 

•24 

»37 

2IO4 

•7i 

28 

472 

.19 

158 

2427 

.69 

26 

440 

.18 

145 

2230 

59.  The  same.  Coronas. — Table  23  contains  the  data  for  the  maxima 
obtainable  with  the  radium  tubelets  I,  II,  III,  IV,  V,  at  my  disposal. 
The  corresponding  corona  was  a  large  orange-yellow  type,  corresponding 
in  my  former  reductions  to  506,000  nuclei  in  the  exhausted  fog  chamber. 
I  have  supposed  this  to  be  equivalent  to  653,000  when  the  fog  chamber 
is  at  atmospheric  pressure,  seeing  that  the  coronas  are  actually  displaced 
during  exhaustion ;  i.  e. ,  at  the  maximum  ionization  does  not  coincide  in 
the  position  with  the  largest  corona  on  exhaustion,*  but  is  displaced  in 
the  direction  of  the  exhaust  currents.  This  would  seem  to  mean  that 
exhaustion  is  more  rapid  than  the  reproduction  of  ions  to  restock  the 
region  of  dilatation.  In  general  this  inherent  discrepancy  of  a  marked 


*See  Chapter  III;  also  Science,  xxvm,  p.  26,  1908. 


ELECTRON    METHOD    OF    STANDARDIZING    CORONAS. 


71 


distribution  of  ionization  increasing  from  end  to  end  of  the  fog  chamber 
is  still  outstanding.  It  is  partially  allowed  for,  since  the  observations 
are  made  near  the  middle  of  the  chamber,  where  the  average  conditions 
supervene. 


FIGS.  20,  22,  24. — Deflection  at  the  electrometer  in  successive  observations 
4  seconds  apart,  for  successive  negative  and  positive  charges  in  the  orders 
of  the  numbers  on  the  curves. 

60.  The  same.  Summary. — The  data  of  table  23  are  given  in  figs.  20 
and  21 ;  fig.  20  merely  shows  the  fall  of  potential  in  scale  readings  in 
the  successive  observations  4  seconds  apart,  for  positive  and  negative 
charges.  Fig.  2 1  gives  the  corresponding  positive  and  negative  apparent 


72        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

ionizations.  If  the  two  curves  between  0.8  and  1.2  volts  be  considered, 
the  mean  ionization  of  each  is 

Apparent  positive  ions,  negative  charge N  —    540,000 

Apparent  negative  ions,  positive  charge A"  =  1,164,000 

Total  true  ionization N  +  N'=  1,704,000 

Total  nuclei  caught 650,000 

It  will  be  seen  that  N+N'  is  the  true  total  ionization  positive  and  nega- 
tive, if  io1V  =  3-4.  Only  65/170,  or  about  38  per  cent,  of  this  is  actually 
caught  in  the  given  fog  chamber  on  exhaustion,  provided  the  old  coronal 
values  are  correct. 

If,  however,  it  is  assumed  that  negative  ions  only  are  caught  during 
exhaustion  in  the  fog  chamber  in  question,  then  the  value  of  the  electron 
would  be 

io100  =  3.4X2.62X-  =  4-4  electrostatic  units. 

61.  Data.     Moderate  ionization.     Electrical  currents. — These   results 
were  obtained  by  placing  but  one  radium  tubelet,  No.  IV,  in  the  alumi- 
num tube  it'  of  the  condenser  fog  chamber  (fig.  19).    The  data  were 
assembled  in  the  same  way  as  the  above,  N  =  Kd(log  V)/dt,  as  usual,  but 
they  are  here  withdrawn,  as  they  are  sufficiently  reproduced  in  the  curves 
(figs.  22  and  23).   In  the  first  and  second  parts  of  the  table  positive  charges 
only  are  treated  and  the  results  show  the  apparent  negative  ionization. 
In  the  third  part  of  table  23,  however,  both  currents  are  observed  in 
succession  and  the  true  total  ionization  is  N  +  N'  as  before.     Moreover, 
in  parts  i  and  2  the  capacity  of  the  condensers  is  widely  varied,  410  to 
1459  cm.,  without  showing  serious  divergence;  though  to  bring  this  effect 
out  fully  both  positive  and  negative  currents  should  have  been  averaged. 

62.  The  same.     Coronas. — At  a  fall  of  pressure  of  2 1  cm.  or  dp/p  =  o.  2  7 , 
the  nucleation  was  stationary  and  equal  to  N=  113,000  in  the  exhausted 
fog  chamber.  At  atmospheric  pressure,  therefore,  113 ,000  X  i  -3  7  =  1 54,000 
nuclei  should  have  been  present.    The  effect  of  a  charge  on  the  core  of 
the  condenser  did  not  appreciably  diminish  the  nucleation  or  at  least  the 
estimate  could  not  be  pushed  below  about  140,000. 

63.  The  same.    Summary. — For  the  case  of  the  third  and  fourth  parts 
of  table  in  question  the  successive  observations  at  intervals  of  30  seconds 
apart  are  shown  in  fig.  22,  the  slopes  only  being  of  interest.    The  appar- 
ent values  of  N  are  given  (fig.  23).     Though  the  positive  and  negative 
currents  are  both  taken  in  one  section  only,  parts  3  and  4,  all  the  four 
series  show  about  the  same  drift,  even  though  taken  many  days  apart. 
The  condenser  effect  (excessive  rapidity  of  needle)  may  be  considered 
eliminated  for  capacities  greater  than  500  cm. 


ELECTRON    METHOD    OF    STANDARDIZING    CORONAS. 


73 


0          •£         *4         -6         '8 
FIGS.  21,  23,  25. — Apparent  ionization,  N  per  cu.  cm. 
corresponding  to  the  different  voltages,  V. 


74   CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 

By  averaging  the  ionizations  between  F  =  o.6  and  F  =  i.24  in  both 
parts  3  and  4  of  the  experiments  made,  the  data  found  are  as  follows : 

Apparent  negative  ions N=*  278,000 

Apparent  positive  ions N'  — 107,000 

True  total  ions N  +  N'  =  385,000 

Total  nuclei 180,000 

Hence  about  47  per  cent  of  all  the  ions  were  caught  on  exhaustion  if  the 
values  of  u,  v,  e,  N,  inserted,  are  correct.  Supposing  that  negative  ions 
only  are  caught  in  the  above  fog  chamber  the  value  of  the  electron  would 
be 

io100  =  3.4X2.i4X-  =  3.6  els.  units. 

2 

64.  Data.    Small  ionizations.     Electric  currents. — In  the  next  series 
the  aluminum  if,  fig.  19,  was  surrounded  by  a  lead  tube  with  walls  0.117 
cm.  thick,  leaving  the  y  rays  only  effective  and  these  much  reduced  in 
intensity.    The  data  are  given  in  figs.  24  and  25. 

65.  The  same.    Coronas. — The  coronas  found  at  a  drop  of  pressure 
similar  to  the  above,  dp/p  =  o.^oo,  corresponded  in  my  reductions  to 
46,200  nuclei  in  the  exhausted  fog  chamber.     Hence  at  atmospheric 
pressure  there  should  have  been  64,000.    The  effect  of  charging  the  core 
was  not  clear;  the  reduction  could  be  estimated  at  51 ,000  at  the  uttermost. 

66.  The  same.    Summary. — The  drop  of  potential  in  scale  parts  in 
successive  intervals  30  cm.  apart  is  given  in  fig.  24,  showing  how  much 
more  slowly  the  negative  charges  are  lost  than  the  positive  charges.   The 
apparent  values  of  N  are  given  in  fig.  25,  to  which  remarks  similar  to 
those  already  made  are  applicable.    There  is  the  usual  drift  and  the  usual 
temporary  fluctuation. 

If  the  mean  data  be  taken  between  V  =  i  .1  and  1.4  volts  the  results  are 

Apparent  positive  ions W—  37,000 

Apparent  negative  ions AT=  98,000 

True  total  ionization AT + AT'- 135,000 

Total  nuclei  caught 60,000 

It  follows,  then,  that  about  44  per  cent  of  the  total  ionization  computed 
from  io10e  =  3.4,  u  and  v,  is  caught  on  condensation. 

If  we  suppose  the  negative  ions  only  are  caught  in  the  above  fog  cham- 
ber, the  electron  value  is 

i 
*Xiol°-3.4Xa.3X  — 3.9  els.  units. 


ELECTRON    METHOD    OF    STANDARDIZING    CORONAS.  7$ 

67.  Conclusion. — Supposing  the  electron  value  to  be  ioloe  =  3.4  electro- 
static units  as  before,  the  normal  velocities  of  the  ions  in  wet  air  to  be 
#  =  1.37,  ^=1.51  cm./sec.  in  the  volt/cm,  field,  the  coronal  value  of  the 
ions  caught  in  the  above  fog  chamber  is  in  the  several  cases 

Total  ions,  1,700,000  Total  nuclei,  38  per  cent. 

385,000  47  per  cent. 

135,000  44  per  cent. 

When  N  is  1,700,000  the  coronas  are  too  diffuse  for  sharp  specification. 
If  it  is  assumed  that  negative  ions  only  are  caught,  and  if  the  nucleations 
corresponding  to  the  coronas  seen  in  the  given  fog  chamber  be  taken  as 
developed  in  my  earlier  work,  then  for  N+N'  =  1,700,000,  385,000,  and 
135,000,  the  electron  values  are  io1V  =  4>4,  3.6,  and  3.9  electrostatic  units. 

With  regard  to  the  two  parts  of  this  paper  that  need  revision  the  first, 
the  comparison  of  the  computed  condenser  capacity  C'  with  a  standard, 
is  a  minor  matter,  but  the  other,  i.  e.,  the  marked  distribution  of  ioni- 
zation  along  the  axis  of  the  fog  chamber,  will  need  further  inquiry.  In 
the  direction  of  the  exhaustion  the  amount  of  ionization  may  vary  in  the 
ratio  of  more  than  i  to  2,  in  a  fog  chamber  of  about  0.5  meter  of  length, 
and  this  under  conditions  where  there  should  apparently  be  no  variations 
and  irrespective  of  the  production  of  radiation  from  within  or  from  out- 
side of  the  fog  chamber.  The  final  question  relating  to  the  drift,  and  the 
asymmetry  of  the  curves  will  be  considered  in  all  its  bearings  in  the  next 
chapter. 


CHAPTER  VI. 

THE  ELECTROMETRIC  MEASUREMENT  OF  THE  VOLTAIC  POTENTIAL  DIFFER. 

ENCE  BETWEEN  THE  TWO  CONDUCTORS  OF  A  CONDENSER, 

SEPARATED  BY  AN  IONIZED  MEDIUM. 

68.  Introductory. — The  difficulties  encountered  in  the  preceding  paper 
(Chapter  V,  section  57),  were  made  the  subject  of  direct  investigation 
by  replacing  the  fog  chamber  with  a  metallic  cylindrical  condenser,  the 
core  of  which  was  an  aluminum  tube  50  cm.  long  and  0.63  cm.  in  diameter, 
the  shell  a  brass  tube  50  cm.  long  and  2.1  cm.  in  diameter,  coaxial  with 
the  former.  Sealed  radium  tubelets  could  be  placed  within  the  aluminum 
tube  or  withdrawn  from  it.  Moreover,  either  the  outer  coat  or  the  core 
of  the  condenser  could  be  joined  in  turn  with  the  Dolezalek  electrometer, 
the  other  being  put  to  earth.  The  conducting  system  now  appears  as 
shown  in  fig.  26,  C  being  the  outer  coat  or  brass  shell,  A  the  aluminum 
core,  and  r  the  radium  tubes  in  the  cylindrical  core.  Conductors  are 
earthed  at  e.  BB  show  the  metallic  connections  with  the  auxiliary  con- 
densers Cf  C" ,  E  is  one  of  the  insulated  quadrants  of  the  electrometer 
with  the  highly  charged  needle  N,  E  being  virtually  also  a  condenser. 

A  Clark  standard  cell  5  may  be  inserted  for  standardization,  but  it  is 
otherwise  withdrawn. 


T        \\        r 

3                           £    r^~,r 

• 

A(    \ 

y  \>  \ 

f- 

C' 

•    = 

1  JZ? 

C           V*, 

FIG.  26. — Disposition  of  cylindrical  condenser  C,  auxiliary  condensers 
C'  C",  key  to  earth  K,  electrometer  E,  standard  cell  5.  All  earthed  at  e 
Diagram. 

Direct  experiment  showed  the  self-charging  tendencies  to  come  appar- 
ently from  the  highly  charged  needle  N,  or  at  least  to  arise  in  the  electro- 
meter E.  Positive  ions  are  lodged  into  the  conductor  EBB  A  for  a  positive 
needle,  negative  ions  for  a  negative  needle.  In  addition  to  this,  how- 
ever, there  is  a  voltaic  difference,  aluminum-brass,  at  AC  when  radium  is 
in  place  and  the  medium  therefore  highly  ionized.  The  latter  potentials 
are  usually  negligible.  These  are  the  chief  electromotive  forces,  the  first 


VOLTAIC    POTENTIAL    DIFFERENCE    BETWEEN    CONDUCTORS. 


77 


very  high  (150  volts)  and  in  a  weakly  ionized  medium,  the  other  low 
(0.2  volt),  but  in  an  intensely  ionized  medium,  but  they  may  eventually 
produce  equal  currents.  Effectively  this  is  the  case.  Other  voltages  such 
as  the  room  potential  may  be  operative,  but  their  effect  proved  to  be 
secondary.  If  the  capacities  C'C",  are  successively  removed,  the  electro- 
meter current  increases  proportionately,  showing  its  origin  to  be  directed 
from  the  needle  or  the  electrometer  case  toward  the  insulated  or  non- 
earthed  pair  of  quadrants. 
60 


FIG.  27. — Increment  of  potential  (cm.  of  scale),  in  the  lapse  of 
time  (seconds),  when  the  auxiliary  condensers  are  successively 
removed. 

FIG.  28. — Variation  of  potential  V  (cm.  of  scale),  in  the  lapse  of 
time  (seconds) ,  when  the  aluminum  core  or  the  brass  shell  of 
the  electrical  condenser  are  alternately  put  to  earth.  Subscript 
zeros  indicate  the  earthed  metal. 

If  the  electrometer  metals  are  reversed  (see  fig.  26),  the  voltaic  couple 
is  reversed.  This  makes  it  possible  to  obtain  both  the  voltaic  contact 
potential  and  the  ionization  in  the  cylindrical  condenser  C,  from  a  pair 
of  commutated  measurements.  If  the  sign  of  the  charge  of  the  electro- 
meter needle  is  reversed,  the  deflection  of  the  needle  is  not  reversed,  but 


78        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

continues  to  grow  indefinitely  in  the  lapse  of  time  in  an  invariable 
direction.  Hence  there  must  be  a  source  of  current  in  the  electrometer, 
as  intimated. 

69.  Theory.  —  Let  Vn  be  the  potential  of  the  needle,  Vc  the  voltaic 
potential  difference  of  the  two  metals  of  the  condenser,  the  shell  being 
put  to  earth,  V  the  potential  of  the  insulated  conductor  BB,  measured 
by  the  electrometer.  Let  n  be  the  apparent  ionization  in  the  electro- 
meter, N  the  (radium)  ionization  in  the  condenser  (length  7,  radii 
Let  C  be  the  total  capacity  of  the  systems  CBBE.  Then 


where  A  is  a  constant,  u  and  v  the  normal  velocities  of  the  positive  and 
negative  ions,  e  the  charge  of  the  electron.  The  needle  is  supposed  to  be 
positively  charged.  This  may  be  written 

V=Va-K(V-Vc) 
where  for  N  =  o,  K  =  o,  or 


i.  e.,  the  current  in  the  electrometer,  observed  in  the  absence  of  radium, 
from  needle  to  quadrants.    This  is  directly  measurable  with  accuracy.    It 
is  nearly  proportional  to  Vn  since  V  is  much  within  i  per  cent  of  Vn. 
The  integral  of  this  equation  is,  t  being  the  time, 

V-  (VJK)(i  -KVJVa)(i  -e-K>) 

the  sign  of  V  is  negative  if  Va  <  KVC,  which  is  the  case  below.  If  there 
is  an  initial  potential  V0  imparted  by  the  standard  cell,  which  is  then 
removed, 


If,  now,  the  needle  is  left  positively  charged,  but  the  condenser  metals 
exchanged  (commutated)  ,  so  that  the  aluminum  core  is  earthed  and  the 
shell  now  put  in  contact  with  the  electrometer  (see  figure)  ,  the  equation 
becomes 

V  =  (VJK)  (i  +  KVe/Vj(i-  e~Kt) 


Here  K  refers  to  the  negative  current  or  normal  velocity  of  negative  ions 
v.  Similarly  let  K'  refer  to  the  normal  velocity  of  positive  ions  u.  Also 
let  «  =  N/K  and  «  =  NIK'.  Then  if  k  =  Ve/*Va,  and  k'  =  Vc/«'Va 


=  Va(i  -kN)e~Kt  V'  =  Va(i+kN)e~Kt 


VOLTAIC    POTENTIAL    DIFFERENCE    BETWEEN    CONDUCTORS.  79 

If  the  potential  V=  V^  at  *  =  oo, 


V 


two  equations  from  which  both  N  and  Vc  may  be  found,  if  the  limiting 
potentials  V^,  V  ^  and  the  electrometer  current  Va  are  severally  observed. 
If  Vx  is  not  obtainable,  it  may  be  computed  from  observations  at  t  and 
tl  =  2t  as 

V^(2V-  V,)  I  V2  and  V'»  =  (2  V  -  V\)  /  V>* 

Here,  however,  there  is  a  difficulty,  as  the  curves  begin  with  a  double 
inflection  not  yet  explained.  The  times  ti  =  2t  must  therefore  be  esti- 
mated from  the  observations  beyond  the  double  inflections,  or  the  rear- 
ward prolongation  of  the  curve  for  those  observations,  to  meet  the  time 
axis.  The  initial  tangents  may  be  found  in  the  same  way,  but  this  is  not 
necessary,  since  their  values  are,  respectively, 

VQ=Va(i-kN)  and  Va(i 
while 

>~Kt 


A  few  other  relations  are  often  useful,  as,  for  instance, 


y  —\r          °°        V  —V   d     V  IV 

K0  —  v  a-t  T>    v  c—  ^ooV1—  v  a/  V  o 


all  of  which,  however,  have  limited  application  because  of  the  initial 
double  inflection  of  the  curves. 

To  solve  the  transcendental  equations  the  times  of  two  observations 
may  be  chosen,  so  that  if  V  and  t,  V  and  tf  correspond,  if  =  2t.    Thus, 


V 
from  which  N  =  «K  follows.    Similarly, 

i       2V-V' 


V2 

00 


If  t'  =  2t  and  fl  =  2tl,  the  initial  double  inflection  may  in  a  measure  be 
ignored  in 

,-*(.-„>_  V-V    V, 
Vi-V\  V 


8o        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


70.  Data.  Origin  of  the  electrometer  current. — The  seat  of  the  chief 
electromotive  force  or  charging  current  in  the  electrometer  follows 
from  the  following  data,  summarized  in  fig.  27,  in  which  the  capacities 
C,  C1 ',  C" ',  fig.  26,  are  successively  removed.  The  currents  increase  in  the 
same  ratio  as  the  reduction  of  capacities,  E  being  that  of  the  electro- 
meter. The  data  are,  potentials  in  scale  parts  (where  i  cm.  is  equivalent 
to  0.0595  volt),  Va  being  the  fall  per  second: 


Capacities. 

Va  in  cm. 

Va  in  volts 
per  sec. 

C+C'  +  C»+E 

0.14 

0.0083 

C'  +  C»  +  E 

•15 

.0089 

C'  +  E 

•58 

•0345 

E 

4-3 

.256 

Time o 

Va o 


12 

3-7 


16 
6.1 


20 

8.7 


24 

II. O 


28 
13-4 


32     60  sec. 

15-5 3!-o  cm. 


The  change  of  voltage  throughout  the  main  contours  of  the  curves 
is  almost  a  linear  variation  with  the  lapse  of  time,  except  that  at  the 
beginning  the  motion  is  accelerated  from  rest  as  usual;  for  instance: 

4         8 
•  3      1.5 

It  is  the  linear  character  of  these  curves  that  greatly  simplifies  the 
following  measurements. 

24.  —  Measurement  of  ionization  N,  and  voltaic  contact  difference  Vc.  Time 
intervals  4  sec.  Aluminum-brass  condenser.  /  =  so  cm.,  2^  =  2.01  cm.,  2/?2  =  0.634 
cm.  Scale  part  cm.  =0.0588  volt.  Radium  I,  II,  III,  IV,  V  in  aluminum  tube. 
N  =1,750,000;  Fc  =  6.37  cm.  or  0.375  volt. 


Deflection. 

(i)  Aluminum  to 
electrometer,  brass 
to  earth. 

(2)  Aluminum  to 
earth,  brass  to 
electrometer. 

(3)  Aluminum  to 
earth,  brass  to 
electrometer. 

(4)  Aluminum  to 
electrometer,  brass 
to  earth. 

0.0 

+  0.0 

0.0 

—  o.o 

—    .  i 

•3 

•  3 

—    .  i 

-    -4 

I  .  2 

1.4 

-    -4 

-    -9 

2-5 

2.7 

-    -9 

-1.4 

4.0 

4-i 

-1.4 

-1.9 

5-0 

5-3 

-1.9 

—  2.2 

5-9 

6-3 

-2.3 

-2.5 

6.6 

6.9 

-2.6 

—  2.7 

7-i 

7-4 

-2.8 

-2.9 

7-5 

7-8 

-2.9 

-3.0 

7.8 

8.0 

-3.0 

-3-1 

8.1 

8.2 

-3-1 

-3-2 

8.3 

8.4 

-3-2 

-3-2 

8-5 

8-5 

-3-3 

-3-3 

8-7 

8.6 

-3-3 

—  3-3 

8.8 

8.7 

*-3.5 

*-3-4 

8-9 

*9.2 

*-3-6 

9.0 

*9-4 

*9.o 

*9.2 

*  After  additional  60  sec. 


VOLTAIC    POTENTIAL    DIFFERENCE    BETWEEN    CONDUCTORS. 


8l 


TABLE  25.  —  Voltaic  contacts,  Al-Zn,  Al-Cu,  A1-A1.  Four-sec,  intervals  (usually)  between 
observations  for  V.  Scale  part  cm.  =0.092  volt.  Va  =  0.0454  cm.  Positive  needle. 
Radium  I  to  V.  K  =  36.1X10  +  °. 


V  for  Al-Zn. 

V  for  Al-Cu. 

V  for  A1-A1. 

Zn  to 
earth. 

Alto 
earth. 

Zn  to 

earth. 

Cu  to 
earth. 

Alto 
earth. 

Cu  to 
earth. 

Shell  to 
earth. 

Core  to 
earth. 

Shell  to 
earth. 

—  o.o 

0.0 

—  o.o 

o.o 

o.o 

o.o 

+  0.0 

+  0.0 

+  0.0 

—      .0 

.0 

—    .0 

—    .  i 

.  i 

—    .  i 

.0 

.0 

.0 

—     .  2 

•4 

—    .  i 

-    -5 

•7 

-    -5 

.0 

.  i 

.0 

-    -3 

.8 

-    -3 

—  1.2 

1.6 

-i-3 

.0 

•3 

.  i 

-    -5 

i-3 

-    -3 

—  2.0 

2.6 

-1.9 

.  i 

.6 

.  2 

-    -7 

i-7 

-    -5 

-2.7 

3-5 

-2.6 

.2 

.8 

•3 

-    -9 

2.0 

-    .6 

-3-2 

4.2 

-3-i 

•3 

•  9 

•4 

—     .0 

2  .  2 

—    .  7 

-3-7 

4-7 

-3-5 

•3 

.  i 

•4 

—      .0 

2-4 

-    -7 

-4.0 

5-1 

-3-8 

•4 

.2 

•  5 

—    .  i 

2-5 

-    .8 

-4.2 

5-4 

-4.1 

•4 

•3 

•  5 

—    .  i 

2.7 

-    .8 

-4.4 

5-7 

-4-3 

•  5 

•  5 

•  5 

—    .  i 

2.8 

-    -9 

-4.6 

5-9 

-4.4 

•  5 

.6 

.6 

—      .2 

2.8 

-    -9 

-4-7 

6.1 

-4-5 

.6 

•  7 

.6 

—     .2 

2.8 

-    -9 

-4.8 

6-3 

-4-7 

.6 

.8 

.6 

—     .  2 

2.9 

-    -9 

-4.9 

6-5 

-4-8 

.6 

•9 

.6 

-      -3 

2.9 

-    -9 

-5-0 

6.6 

-4.8 

*.6 

•9 

.6 

*-      -3 

*3-o 

—  i.o 

*5-3 

*6.9 

*-5-2 

.9 

*.8 

*i.i 

*5-3 

*6.9 

*-5-2 

*2.I 

.8 

*  After  further  60  sec. 


FIG.  29. — Variation  of  potential  (cm.  of  scale)  in  the  lapse  of  seconds  for 
aluminum-copper,  aluminum-zinc,  and  aluminum-aluminum  condensers. 
Subscript  zeros  show  the  earthed  metal. 


82        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

71.  Aluminum  core  charged  with  radium  tubelets  I-V.     Data. — The 

air  in  the  condenser  C  is  now  highly  ionized  and  its  voltage  becomes 
appreciable.  The  data  obtained  are  given  in  table  24  and  fig.  28.  The 
needle  is  positively  charged  thus  (virtually)  impelling  positive  ions  to- 
ward the  quadrants  of  the  condenser.  In  the  four  series  of  data  observed 
the  aluminum  core  of  the  condenser  is  twice  joined  to  the  electrometer, 
the  brass  shell  being  put  to  earth  (series  i  and  4)  and  twice  commutated 
(aluminum  to  earth  series  2  and  3).  The  results  are  identical,  except  that 
in  series  3  the  insulation  was  perhaps  better.  The  accelerated  march  of 
the- needle  from  rest  is  obvious  in  both  curves  and  is  thus  independent  of 
the  sign  of  the  limiting  voltage  V^.  It  may  be  mere  inertia,  but  it  is  of 
less  consequence  here  because  the  initial  data  are  not  needed  in  the 
computation  of  table  25. 

72.  Results.    lonization  N.    Voltaic  contact  potential  difference  Vc. — 

The  equations 


rf 

00 


may  now  be  used  to  compute  N  and  Vc.    The  constants  are  numerically 
(all  in  scale  parts,  i  cm.  equivalent  to  0.0595  volt) 

K  =  36.iXioe      ^=-3.45       Fa  =  o.i42      K'  =  39.7Xio6        V'w=+9.3 

Hence 

N  =*  1,750,000  ions,  either  positive  or  negative. 
^  =  6.37  cm.,  or  0.38  volt. 

73.  Voltaic  contacts:  aluminum-zinc,  aluminum-copper,  aluminum- 
aluminum. — The  results  obtained  for  aluminum-brass  made  it  desirable 
to  investigate  similar  cases  for  other  metals  and  zinc ;  copper  and  alumi- 
num suggested  themselves.  These  were  used  in  form  of  thin  sheets  of 
the  metal,  bent  into  cylindrical  shells  about  as  large  as  the  above  brass 
shell.  No  special  care  was  here  taken  to  secure  accurate  diameters, 
nor  to  prepare  the  metal  surfaces.  The  aluminum  core  with  the  radium 
tubelets  (I  to  V)  within,  was  the  same  as  heretofore.  The  data  are  shown 
in  table  25  and  in  fig.  29.  All  potentials  are  given  in  scale  parts  where 
i  cm.  is  equivalent  to  0.092  volt.  The  charging  current  for  the  electro- 
meter, found  in  the  absence  of  radium  before  and  after  these  experiments, 
was  Va  =  0.0454  cm. 

Since  we  may  write  algebraically 

tf -?..»«/ (V'.+  f,) 
and 


VOLTAIC    POTENTIAL    DIFFERENCE    BETWEEN    CONDUCTORS. 


remembering  that  V^is  negative,  while  V ^  is  positive,  the  following  data 
appear: 


Couple. 

N 

vc 

vx 

v* 

Al-Cu  

s,o  50,000 

Volt. 
o.  5  58 

cm. 
—  5-25 

cm. 
+  6.00 

Al-Zn 

I  7QO  OOO 

IQI 

—  I    17 

300 

A1-A1 

i  140  ooo 

06  «? 

+  O   T\ 

2    I  5 

The  large  nucleation  obtained  here  for  copper  remains  unexplained. 
It  was  somewhat  reduced  in  other  similar  experiments,  but  remained 
high.  Since  V'^-f  V ^  =  1.65,  slight  differences  in  contact  would  produce 
a  serious  effect.  From  these  data  it  follows,  finally,  that  the  voltaic 
contact  zinc-copper  is  0.367  volt.  After  cleansing  with  acids  data  like 
Al-Cu  =  o.58  volt,  Al-Zn  =  o.o6  volt,  or  Zn-Cu  =  o-52  volt  were  obtained, 
which  varied  again  after  other  treatment. 

74.  Further  experiments.  Conclusion. — In  addition  to  the  above 
experiments,  a  great  variety  were  made,  as,  for  instance,  with  weaker 
radium  (single  tubelets)  in  the  core  of  the  condenser;  with  radium  inside 
and  outside  of  the  condenser;  with  the  metal  surfaces  cleansed  with  acids, 
or  polished,  or  aged,  etc.  A  few  data  may  be  referred  to  here. 

The  highest  nucleation  for  an  aluminum  core  charged  with  radium 
tubelets  occurs  in  case  of  a  copper  envelope  for  the  condenser.  Some- 
what smaller  values  occur  for  zinc  and  brass,  and  the  smallest  for  alumi- 
num shells.  The  agreement  is  usually  unsatisfactory.  The  voltaic  con- 
tacts are  such  as  to  place  zinc-copper  at  0.4  to  0.6  volt.  The  data  for 
groups  of  radium  tubes  are  larger  than  the  values  computed  from  indi- 
vidual tubes,  N  =  \/N12+AV+  .  .  .  .,  probably  from  the  effect  of 
secondary  radiation  and  non-uniform  ionization.  We  may  also  ascribe 
the  high  ionization  in  a  copper  shell  as  compared  with  a  low  ionization 
in  an  aluminum  shell  to  the  same  cause.  If  the  radium  is  placed  without 
the  condenser  the  voltaic  contacts  do  not  appreciably  differ  from  the 
values  found  when  the  radium  tubelets  lie  in  the  core.  One  may  note 
that  even  in  the  aluminum-aluminum  condenser  the  voltaic  contact  is 
not  zero  but  about  0.05  volt.  In  other  instances  non-commutated  electro- 
motive forces  often  appear.  The  contact  Al-Zn  is  peculiarly  variable  even 
as  to  sign. 

As  a  whole  these  experiments  lead  to  no  general  conclusion  of  relevancy 
here  and  they  have  therefore  been  withheld  from  detailed  consideration. 

Finally,  to  detect  the  source  of  the  electromotive  force  in  the  electro- 
meter, this  was  replaced  by  another  instrument,  No.  2,  of  the  same  kind, 


84        CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

as  soon  as  it  could  be  obtained.  The  absence  of  electric  current  Va  =  o 
in  the  new  instrument  and  its  presence  in  the  old  electrometer  made  it 
necessary  to  overhaul  the  latter.  It  was  eventually  found  that  the  brass 
case  had  been  insufficiently  earthed,*  so  that  a  current  from  the  Zamboni 
cell,  breaking  through  the  hard  rubber  insulation  at  the  top  of  the  quartz- 
fiber  suspension  kept  the  case  charged  to  a  high-constant  potential. 
This  charge  thereupon  gradually  leaked  into  the  insulated  quadrant 
through  the  amber  insulators,  producing  the  current  Va  corresponding 
to  the  sign  of  the  electrode  of  the  Zamboni  pile  and  of  the  electrometer 
needle.  On  providing  the  case  of  the  old  electrometer  with  a  well-earthed 
clamp,  the  current  Va  vanished.  The  new  electrometer  did  not  show  this 
defect  even  when  the  case  was  not  specially  earthed,  whereas  any  insu- 
lation of  the  old  electrometer  immediately  restored  Va. 

Fortunately,  however,  Va  is  so  remarkably  constant  that  it  can 
actually  be  used  in  the  measurements  with  advantage,  as  was  done  in  the 
present  chapter,  or  eliminated  by  commutation,  as  was  done  in  Chapter  V. 

*Probably  owing  to  a  thin  film  of  varnish  which  had  escaped  detection.  The  room 
was  so  dry  that  no  discharge  occurred  through  the  feet  of  the  instrument. 


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